## Bai, Zhi-Dong

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 Author ID: bai.zhi-dong Published as: Bai, Zhidong; Bai, Z. D.; Bai, Zhi-Dong; Bai, Zhi Dong; Bai, ZhiDong; Bai, Zhi-dong more...less Homepage: https://twas.org/sites/default/files/thth7_1.pdf External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 239 Publications since 1981, including 6 Books 1 Contribution as Editor · 1 Further Contribution Reviewing Activity: 18 Reviews Biographic References: 10 Publications Co-Authors: 139 Co-Authors with 219 Joint Publications 4,862 Co-Co-Authors
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### Co-Authors

 19 single-authored 24 Zhao, Lincheng 18 Hu, Jiang 18 Krishnaiah, Paruchuri Rama 16 Wu, Yuehua 14 Rao, Calyampudi Radhakrishna 14 Yao, Jianfeng 14 Yin, Y.-Q. 14 Zheng, Shurong 12 Silverstein, Jack W. 9 Hu, Feifang 9 Miao, Bai-qi 8 Chen, Xiru 8 Wong, Wing-Keung 7 Pan, Guangming 6 Jiang, Dandan 6 Wang, Chen 6 Zhou, Wang 5 Babu, Gutti Jogesh 5 Chen, Guijing 5 Hwang, Hsien-Kuei 5 Li, Huiqin 5 Liang, Wenqi 5 Su, Chun 5 Yin, Yanqing 5 Zhang, Baoxue 4 Chen, Zehua 4 Choi, Kwok Pui 4 Fujikoshi, Yasunori 4 Jin, Baisuo 4 Li, Hua 4 Li, Weiming 4 Liu, Tianqing 3 Cheng, Philip E. 3 Chow, Mosuk 3 He, Xuming 3 Hu, Guorong 3 Kundu, Debasis 3 Liang, Yingchang 3 Liu, Huixia 3 Tsai, Tsung-Hsi 3 Tsay, Jhishen 3 Xia, Ningning 3 Zhang, Li-Xin 3 Zhao, Ningning 2 Biswas, Atanu 2 Chao, Chern-Ching 2 Chen, Jiaqi 2 Fu, James C. 2 Guo, Meihui 2 Harding, Matthew C. 2 Hui, Yongchang 2 Li, Gang 2 Liu, Yan 2 Nair, K. Krishnan 2 Qin, Yingli 2 Sarkar, Sanat Kumar 2 Subramanyam, Kasala 2 Wang, Wenjin 2 Wang, Xiaoying 2 Xu, Daming 2 Zen, Mei-Mei 2 Zhang, Bingzhi 2 Zhang, Chao 2 Zhang, Qiuyan 1 An, Hongzhi 1 Andrews, George Eyre 1 Bai, Li 1 Brockwell, Peter J. 1 Chang, Lo-Bin 1 Chen, Changhua 1 Chen, Ling 1 Chen, Yang 1 Chen, Yuming 1 Chen, Yuming 1 Cheng, Yu 1 Chernoff, Herman 1 Couillet, Romain 1 Cui, Wenquan 1 Davis, Richard A. 1 Debbah, Mérouane 1 Devroye, Luc P. J. A. 1 Ding, Xue 1 Du, Xiangjun 1 Du, Yanyi 1 Eddy, William F. 1 Fang, Zhaoben 1 Frieden, Roy B. 1 Fu, Liya 1 Hou, Zhiqiang 1 Hsing, Tailen 1 Hua, Dunming 1 Huang, Suyun 1 Hwang, Chii-Ruey 1 Lee, Sungchul 1 Li, Heng 1 Lin, Zhengyan 1 Lo Huang, Mong-Na 1 Lou, W. Y. Wendy 1 Luo, Wenya 1 Lv, Zhihui ...and 40 more Co-Authors
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### Serials

 23 Journal of Multivariate Analysis 14 Statistics & Probability Letters 11 The Annals of Probability 11 Journal of Statistical Planning and Inference 11 Statistica Sinica 9 The Annals of Statistics 9 Bernoulli 7 The Annals of Applied Probability 6 Annals of the Institute of Statistical Mathematics 6 Sankhyā. Series A. Methods and Techniques 6 Scientia Sinica. Series A 6 Statistical Papers 4 Probability Theory and Related Fields 4 Electronic Journal of Probability 4 Science China. Mathematics 4 Random Matrices: Theory and Applications 3 IEEE Transactions on Information Theory 3 Acta Mathematica Sinica 3 Biometrika 3 Sankhyā. Series B. Methodological 3 Journal of Mathematical Research & Exposition 3 Chinese Annals of Mathematics. Series A 3 Communications in Statistics. Theory and Methods 3 Journal of the Korean Statistical Society 2 Journal of Statistical Physics 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Theory of Probability and its Applications 2 Acta Mathematicae Applicatae Sinica 2 Chinese Annals of Mathematics. Series B 2 Statistics 2 Journal of Theoretical Probability 2 SIAM Journal on Matrix Analysis and Applications 2 Random Structures & Algorithms 2 Proceedings of the National Academy of Sciences of the United States of America 2 Stochastic Processes and their Applications 2 Kexue Tongbao 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Test 1 Advances in Applied Probability 1 The Canadian Journal of Statistics 1 Physics Letters. A 1 Hiroshima Mathematical Journal 1 Journal of the American Statistical Association 1 Journal of Combinatorics, Information & System Sciences 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Journal of Mathematics. Wuhan University 1 Journal of Time Series Analysis 1 Journal of Northeast Normal University. Natural Science Edition 1 Acta Mathematicae Applicatae Sinica. English Series 1 Science Exploration 1 Chinese Journal of Applied Probability and Statistics 1 Journal of China University of Science and Technology 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 Communications in Statistics. Simulation and Computation 1 Notices of the American Mathematical Society 1 Computational Statistics and Data Analysis 1 Mathematical Methods of Statistics 1 Mathematical Finance 1 Australian & New Zealand Journal of Statistics 1 Far East Journal of Theoretical Statistics 1 The Econometrics Journal 1 Acta Mathematica Sinica. English Series 1 Quantitative Finance 1 International Mathematical Journal 1 Journal of Systems Science and Complexity 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Lecture Notes in Statistics 1 Cambridge Series in Statistical and Probabilistic Mathematics 1 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 1 Frontiers of Mathematics in China 1 Electronic Journal of Statistics 1 Sankhyā 1 Mathematics Monograph Series 1 Springer Series in Statistics
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### Fields

 188 Statistics (62-XX) 114 Probability theory and stochastic processes (60-XX) 42 Linear and multilinear algebra; matrix theory (15-XX) 14 Numerical analysis (65-XX) 11 Information and communication theory, circuits (94-XX) 4 History and biography (01-XX) 4 Computer science (68-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

185 Publications have been cited 3,779 times in 2,095 Documents Cited by Year
Spectral analysis of large dimensional random matrices. 2nd ed. Zbl 1301.60002
Bai, Zhidong; Silverstein, Jack W.
2010
Effect of high dimension: by an example of a two sample problem. Zbl 0848.62030
1996
Methodologies in spectral analysis of large dimensional random matrices, a review. (With comments and rejoinder). Zbl 0949.60077
Bai, Z. D.
1999
CLT for linear spectral statistics of large-dimensional sample covariance matrices. Zbl 1063.60022
Bai, Z. D.; Silverstein, Jack W.
2004
Limit of the smallest eigenvalue of a large dimensional sample covariance matrix. Zbl 0779.60026
Bai, Z. D.; Yin, Y. Q.
1993
No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Zbl 0937.60017
Bai, Z. D.; Silverstein, Jack W.
1998
On the empirical distribution of eigenvalues of a class of large dimensional random matrices. Zbl 0833.60038
Silverstein, Jack W.; Bai, Z. D.
1995
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Zbl 0627.62022
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1988
Corrections to LRT on large-dimensional covariance matrix by RMT. Zbl 1360.62286
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2009
Circular law. Zbl 0871.62018
Bai, Z. D.
1997
Ranked set sampling. Theory and applications. Zbl 1045.62007
Chen, Zehua; Bai, Zhidong; Sinha, Bimal K.
2004
Spectral analysis of large dimensional random matrices. Zbl 1196.60002
Bai, Zhidong; Silverstein, Jack W.
2006
Central limit theorems for eigenvalues in a spiked population model. Zbl 1274.62129
Bai, Zhidong; Yao, Jian-Feng
2008
Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix. Zbl 0677.60038
Bai, Z. D.; Yin, Y. Q.
1988
Marcinkiewicz strong laws for linear statistics. Zbl 0960.60026
Bai, Z. D.; Cheng, Philip E.
2000
$$M$$-estimation of multivariate linear regression parameters under a convex discrepancy function. Zbl 0820.62048
Bai, Z. D.; Rao, C. Radhakrishna; Wu, Y.
1992
A note on the largest eigenvalue of a large dimensional sample covariance matrix. Zbl 0652.60040
Bai, Z. D.; Silverstein, Jack W.; Yin, Y. Q.
1988
Large sample covariance matrices and high-dimensional data analysis. Zbl 1380.62011
Yao, Jianfeng; Zheng, Shurong; Bai, Zhidong
2015
Large sample covariance matrices without independence structures in columns. Zbl 1135.62009
Bai, Zhidong; Zhou, Wang
2008
Asymptotics in randomized urn models. Zbl 1059.62111
Bai, Zhi-Dong; Hu, Feifang
2005
On sample eigenvalues in a generalized spiked population model. Zbl 1301.62049
Bai, Zhidong; Yao, Jianfeng
2012
Asymptotic distributions of the maximal depth estimators for regression and multivariate location. Zbl 1007.62009
Bai, Zhi-Dong; He, Xuming
1999
Convergence rate of expected spectral distributions of large random matrices. I: Wigner matrices. Zbl 0779.60024
Bai, Z. D.
1993
Kernel estimators of density function of directional data. Zbl 0669.62015
Bai, Z. D.; Rao, C. Radhakrishna; Zhao, L. C.
1988
On asymptotics of eigenvectors of large sample covariance matrix. Zbl 1162.15012
Bai, Z. D.; Miao, B. Q.; Pan, G. M.
2007
Asymptotic theorems for urn models with nonhomogeneous generating matrices. Zbl 0954.62014
Bai, Z. D.; Hu, Feifang
1999
On detection of the number of signals in presence of white noise. Zbl 0617.62055
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
Convergence rate of expected spectral distributions of large random matrices. II: Sample covariance matrices. Zbl 0779.60025
Bai, Z. D.
1993
Exact separation of eigenvalues of large dimensional sample covariance matrices. Zbl 0964.60041
Bai, Z. D.; Silverstein, Jack W.
1999
Convergence to the semicircle law. Zbl 0648.60030
Bai, Z. D.; Yin, Y. Q.
1988
On the convergence of the spectral empirical process of Wigner matrices. Zbl 1101.60012
Bai, Z. D.; Yao, J.
2005
Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory. Zbl 1185.91155
Bai, Zhidong; Liu, Huixia; Wong, Wing-Keung
2009
Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. Zbl 1312.62074
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2015
Probability inequalities. Zbl 1221.60001
Lin, Zhengyan; Bai, Zhidong
2010
The complete convergence for partial sums of i.i.d. random variables. Zbl 0554.60039
Bai, Zhidong; Su, Chun
1985
Asymptotic properties of adaptive designs for clinical trials with delayed response. Zbl 1012.62087
Bai, Z. D.; Hu, Feifang; Rosenberger, William F.
2002
Gaussian approximation theorems for urn models and their applications. Zbl 1014.60025
Bai, Z. D.; Hu, Feifang; Zhang, Li-Xin
2002
Asymptotic theory of least distances estimate in multivariate linear models. Zbl 0714.62048
Bai, Z. D.; Chen, X. R.; Miao, B. Q.; Rao, C. Radhakrishna
1990
On testing the equality of high dimensional mean vectors with unequal covariance matrices. Zbl 1396.62106
Hu, Jiang; Bai, Zhidong; Wang, Chen; Wang, Wei
2017
Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Zbl 0586.60021
Bai, Z. D.; Yin, Y. Q.
1986
On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Zbl 1373.62245
Bai, Zhidong; Chen, Jiaqi; Yao, Jianfeng
2010
On detection of the number of signals when the noise covariance matrix is arbitrary. Zbl 0617.62056
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
Convergence rates of spectral distributions of large sample covariance matrices. Zbl 1059.60036
Bai, Z. D.; Miao, Baiqi; Yao, Jian-feng
2003
Testing the independence of sets of large-dimensional variables. Zbl 1256.62033
Jiang, DanDan; Bai, ZhiDong; Zheng, ShuRong
2013
On rates of convergence of efficient detection criteria in signal processing with white noise. Zbl 0677.94001
Bai, Zhi-Dong; Krishnaiah, Paruchuri R.; Zhao, Lin-Cheng
1989
Limiting behavior of $$M$$-estimators of regression coefficients in high dimensional linear models. I: Scale-dependent case. II: Scale-invariant case. Zbl 0816.62025
Bai, Z. D.; Wu, Y.
1994
A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices. Zbl 1360.62290
Hu, Jiang; Bai, ZhiDong
2016
Limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1296.60006
Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2014
CLT for linear spectral statistics of Wigner matrices. Zbl 1188.15032
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2009
Maxima in hypercubes. Zbl 1080.60007
Bai, Zhi-Dong; Devroye, Luc; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2005
Convergence rates of the spectral distributions of large Wigner matrices. Zbl 0987.60050
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
2002
No eigenvalues outside the support of the limiting spectral distribution of information-plus-noise type matrices. Zbl 1248.15028
Bai, Zhidong; Silverstein, Jack W.
2012
Estimation of spiked eigenvalues in spiked models. Zbl 1251.15037
Bai, Zhidong; Ding, Xue
2012
An adaptive design for multi-arm clinical trials. Zbl 1011.62079
Bai, Z. D.; Hu, Feifang; Shen, Liang
2002
Limiting behavior of the eigenvalues of a multivariate F matrix. Zbl 0531.62018
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1983
Testing linear hypotheses in high-dimensional regressions. Zbl 1440.62215
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2013
Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis. Zbl 1395.62119
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
Model selection with data-oriented penalty. Zbl 0926.62045
Bai, Z. D.; Rao, C. R.; Wu, Y.
1999
An efficient algorithm for estimating the parameters of superimposed exponential signals. Zbl 1030.62062
Bai, Z. D.; Rao, C. R.; Chow, M.; Kundu, D.
2003
General $$M$$-estimation. Zbl 0890.62050
Bai, Z. D.; Wu, Y.
1997
Functional CLT for sample covariance matrices. Zbl 1210.60025
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2010
On the semicircular law of large-dimensional random quaternion matrices. Zbl 1353.60024
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2016
On the limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0676.62021
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
Statistical analysis for rounded data. Zbl 1162.62012
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2009
Edgeworth expansion of a function of sample means. Zbl 0741.62016
Bai, Z. D.; Rao, C. Radhakrishna
1991
On the theory of ranked-set sampling and its ramifications. Zbl 1008.62023
Bai, Zhidong; Chen, Zehua
2003
Asymptotic normality of minimum $$L_ 1$$-norm estimates in linear models. Zbl 0728.62068
Chen, Xiru; Bai, Zhidong; Zao, Lincheng; Wu, Yuehua
1990
On limit theorem for the eigenvalues of product of two random matrices. Zbl 1108.15022
Bai, Z. D.; Miao, Baiqi; Jin, Baisuo
2007
Strong consistency of the information criterion for model selection in multivariate analysis. Zbl 0678.62064
Nishii, Ryuei; Bai, Zhidong; Krishnaiah, Paruchuri R.
1988
Analysis of rounded data from dependent sequences. Zbl 1432.62065
Zhang, Baoxue; Liu, Tianqing; Bai, Z. D.
2010
On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. Zbl 0657.62058
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1986
A theorem of Feller revisited. Zbl 0669.60034
Bai, Z. D.
1989
Normal approximations of the number of records in geometrically distributed random variables. Zbl 0961.60040
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Liang, Wen-Qi
1998
Mixtures of global and local Edgeworth expansions and their applications. Zbl 0864.62006
Babu, Gutti Jogesh; Bai, Z. D.
1996
On the limit of extreme eigenvalues of large dimensional random quaternion matrices. Zbl 1331.15022
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2014
On the variance of the number of maxima in random vectors and its applications. Zbl 0941.60021
Bai, Zhi-Dong; Chao, Chern-Ching; Hwang, Hsien-Kuei; Liang, Wen-Qi
1998
A chi-square test for dimensionality with non-Gaussian data. Zbl 1032.62054
Bai, Z. D.; He, Xuming
2004
Limit theorems for the number of maxima in random samples from planar regions. Zbl 0986.60007
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Liang, Wen-Qi; Tsai, Tsung-Hsi
2001
A note on the convergence rate of the spectral distributions of large random matrices. Zbl 0894.60034
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
1997
The exact and limiting distributions for the number of successes in success runs within a sequence of Markov-dependent two-state trials. Zbl 1067.60064
Fu, James C.; Lou, W. Y. Wendy; Bai, Zhi-Dong; Li, Gang
2002
Limiting behavior of eigenvectors of large Wigner matrices. Zbl 1235.82035
Bai, Z. D.; Pan, G. M.
2012
Inference on multiple correlation coefficients with moderately high dimensional data. Zbl 1336.62157
Zheng, Shurong; Jiang, Dandan; Bai, Zhidong; He, Xuming
2014
Estimation of the population spectral distribution from a large dimensional sample covariance matrix. Zbl 1278.62079
Li, Weiming; Chen, Jiaqi; Qin, Yingli; Bai, Zhidong; Yao, Jianfeng
2013
The optimal ranked-set sampling scheme for parametric families. Zbl 0972.62053
Chen, Zehua; Bai, Zhidong
2000
An extension of the Hardy-Littlewood strong law. Zbl 1067.60501
Bai, Zhidong; Cheng, Philip E.; Zhang, Cun-Hui
1997
Analysis of rounded data in mixture normal model. Zbl 1254.62023
Zhao, Ningning; Bai, Zhidong
2012
Least absolute deviations analysis of variance. Zbl 0727.62073
Bai, Z. D.; Radhakrishna Rao, C.; Yin, Y. Q.
1990
Asymptotic properties of eigenmatrices of a large sample covariance matrix. Zbl 1234.15013
Bai, Z. D.; Liu, H. X.; Wong, W. K.
2011
CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications. Zbl 1375.60066
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2017
Rooted edges of a minimal directed spanning tree on random points. Zbl 1094.60004
Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.
2006
Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices. Zbl 1309.15055
Yin, Yanqing; Bai, Zhidong
2014
On the maximum-likelihood estimator for the location parameter of a Cauchy distribution. Zbl 0624.62032
Bai, Z. D.; Fu, J. C.
1987
Eigen-inference for energy estimation of multiple sources. Zbl 1366.62107
Couillet, Romain; Silverstein, Jack W.; Bai, Zhidong; Debbah, Mérouane
2011
Rank regression for analysis of clustered data: a natural induced smoothing approach. Zbl 1464.62074
Fu, Liya; Wang, You-Gan; Bai, Zhidong
2010
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix. Zbl 1285.15018
Xia, Ningning; Qin, Yingli; Bai, Zhidong
2013
Semicircle law for Hadamard products. Zbl 1139.15012
Bai, Z. D.; Zhang, L. X.
2007
Convergence of the empirical spectral distribution function of beta matrices. Zbl 1319.60006
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2015
The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix. Zbl 1200.15020
Bai, Z. D.; Zhang, L. X.
2010
Rounded data analysis based on ranked set sample. Zbl 1440.62086
Li, Weiming; Liu, Tianqing; Bai, Zhidong
2012
Extreme eigenvalues of large dimensional quaternion sample covariance matrices. Zbl 1311.60036
Li, Huiqin; Bai, Zhidong
2015
CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data. Zbl 1486.60048
Zou, Tingting; Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng; Zhu, Hongtu
2022
Generalized four moment theorem and an application to CLT for spiked eigenvalues of high-dimensional covariance matrices. Zbl 1475.60014
Jiang, Dandan; Bai, Zhidong
2021
Partial generalized four moment theorem revisited. Zbl 1472.60010
Jiang, Dandan; Bai, Zhidong
2021
Test on the linear combinations of covariance matrices in high-dimensional data. Zbl 1477.62139
Bai, Zhidong; Hu, Jiang; Wang, Chen; Zhang, Chao
2021
Bayesian statistical inference based on rounded data. Zbl 07552566
Zhao, Ningning; Bai, Zhidong
2020
Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices. Zbl 1466.60008
Bai, Zhidong; Li, Huiqin; Pan, Guangming
2019
Invariant test based on the modified correction to LRT for the equality of two high-dimensional covariance matrices. Zbl 1418.62242
Zhang, Qiuyan; Hu, Jiang; Bai, Zhidong
2019
On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality. Zbl 1407.62203
Niu, Zhenzhen; Hu, Jiang; Bai, Zhidong; Gao, Wei
2019
Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices. Zbl 1420.62235
Xia, Ningning; Bai, Zhidong
2019
Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis. Zbl 1395.62119
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
Multi-sample test for high-dimensional covariance matrices. Zbl 07416439
Zhang, Chao; Bai, Zhidong; Hu, Jiang; Wang, Chen
2018
Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT. Zbl 1411.62130
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
Estimating the number of sources in magnetoencephalography using spiked population eigenvalues. Zbl 1398.62353
Yao, Zhigang; Zhang, Ye; Bai, Zhidong; Eddy, William F.
2018
A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test. Zbl 1420.62291
Bai, Zhidong; Pan, Guangming; Yin, Yanqing
2018
On testing the equality of high dimensional mean vectors with unequal covariance matrices. Zbl 1396.62106
Hu, Jiang; Bai, Zhidong; Wang, Chen; Wang, Wei
2017
CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications. Zbl 1375.60066
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2017
Test on the linear combinations of mean vectors in high-dimensional data. Zbl 1369.62122
Li, Huiqin; Hu, Jiang; Bai, Zhidong; Yin, Yanqing; Zou, Kexin
2017
A new nonlinearity test to circumvent the limitation of Volterra expansion with application. Zbl 1390.62176
Hui, Yongchang; Wong, Wing-Keung; Bai, Zhidong; Zhu, Zhen-Zhen
2017
A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices. Zbl 1360.62290
Hu, Jiang; Bai, ZhiDong
2016
On the semicircular law of large-dimensional random quaternion matrices. Zbl 1353.60024
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2016
Convergence of empirical spectral distributions of large dimensional quaternion sample covariance matrices. Zbl 1400.60007
Li, Huiqin; Bai, Zhi Dong; Hu, Jiang
2016
Large sample covariance matrices and high-dimensional data analysis. Zbl 1380.62011
Yao, Jianfeng; Zheng, Shurong; Bai, Zhidong
2015
Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. Zbl 1312.62074
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2015
Convergence of the empirical spectral distribution function of beta matrices. Zbl 1319.60006
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2015
Extreme eigenvalues of large dimensional quaternion sample covariance matrices. Zbl 1311.60036
Li, Huiqin; Bai, Zhidong
2015
Functional CLT of eigenvectors for large sample covariance matrices. Zbl 1309.15054
Xia, Ningning; Bai, Zhidong
2015
A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1333.60025
Bai, Zhidong; Wang, Chen
2015
Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China. Zbl 1398.62276
Bai, Zhidong; Li, Hua; McAleer, Michael; Wong, Wing-Keung
2015
Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix. Zbl 1328.60088
Wang, Chen; Jin, Baisuo; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2015
Convergence rates of spectral distributions of large dimensional quaternion sample covariance matrices. Zbl 1312.15052
Li, Huiqin; Bai, Zhidong
2015
Limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1296.60006
Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2014
On the limit of extreme eigenvalues of large dimensional random quaternion matrices. Zbl 1331.15022
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2014
Inference on multiple correlation coefficients with moderately high dimensional data. Zbl 1336.62157
Zheng, Shurong; Jiang, Dandan; Bai, Zhidong; He, Xuming
2014
Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices. Zbl 1309.15055
Yin, Yanqing; Bai, Zhidong
2014
Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics. Random matrix theory and its applications. Zbl 1288.15046
Bai, Zhidong; Fang, Zhaoben; Liang, Ying-Chang
2014
CLT for linear spectral statistics of a rescaled sample precision matrix. Zbl 1330.15045
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2014
Testing the independence of sets of large-dimensional variables. Zbl 1256.62033
Jiang, DanDan; Bai, ZhiDong; Zheng, ShuRong
2013
Testing linear hypotheses in high-dimensional regressions. Zbl 1440.62215
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2013
Estimation of the population spectral distribution from a large dimensional sample covariance matrix. Zbl 1278.62079
Li, Weiming; Chen, Jiaqi; Qin, Yingli; Bai, Zhidong; Yao, Jianfeng
2013
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix. Zbl 1285.15018
Xia, Ningning; Qin, Yingli; Bai, Zhidong
2013
Asymptotic error bounds for kernel-based Nyström low-rank approximation matrices. Zbl 1349.62262
Chang, Lo-Bin; Bai, Zhidong; Huang, Su-Yun; Hwang, Chii-Ruey
2013
Analysis of rounded data in measurement error regression. Zbl 1294.62034
Zhao, Ningning; Bai, Z. D.
2013
On sample eigenvalues in a generalized spiked population model. Zbl 1301.62049
Bai, Zhidong; Yao, Jianfeng
2012
No eigenvalues outside the support of the limiting spectral distribution of information-plus-noise type matrices. Zbl 1248.15028
Bai, Zhidong; Silverstein, Jack W.
2012
Estimation of spiked eigenvalues in spiked models. Zbl 1251.15037
Bai, Zhidong; Ding, Xue
2012
Limiting behavior of eigenvectors of large Wigner matrices. Zbl 1235.82035
Bai, Z. D.; Pan, G. M.
2012
Analysis of rounded data in mixture normal model. Zbl 1254.62023
Zhao, Ningning; Bai, Zhidong
2012
Rounded data analysis based on ranked set sample. Zbl 1440.62086
Li, Weiming; Liu, Tianqing; Bai, Zhidong
2012
Convergence rates to the Marchenko-Pastur type distribution. Zbl 1234.60033
Bai, Zhidong; Hu, Jiang; Zhou, Wang
2012
Asymptotic properties of eigenmatrices of a large sample covariance matrix. Zbl 1234.15013
Bai, Z. D.; Liu, H. X.; Wong, W. K.
2011
Eigen-inference for energy estimation of multiple sources. Zbl 1366.62107
Couillet, Romain; Silverstein, Jack W.; Bai, Zhidong; Debbah, Mérouane
2011
A note on rate of convergence in probability to semicircular law. Zbl 1244.60022
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2011
Rounded data analysis based on multi-layer ranked set sampling. Zbl 1271.62118
Li, Wei Ming; Bai, Zhi Dong
2011
The mean-variance ratio test – a complement to the coefficient of variation test and the Sharpe ratio test. Zbl 1219.62030
Bai, Zhidong; Wang, Keyan; Wong, Wing-Keung
2011
Analysis of accumulated rounding errors in autoregressive processes. Zbl 1294.62182
Li, Weiming; Bai, Z. D.
2011
Super efficient frequency estimation. Zbl 1213.62098
Kundu, Debasis; Bai, Zhidong; Nandi, Swagata; Bai, Li
2011
Multivariate causality tests with simulation and application. Zbl 1219.62094
Bai, Zhidong; Li, Heng; Wong, Wing-Keung; Zhang, Bingzhi
2011
Test statistics for prospect and Markowitz stochastic dominances with applications. Zbl 1219.91149
Bai, Zhidong; Li, Hua; Liu, Huixia; Wong, Wing-Keung
2011
Spectral analysis of large dimensional random matrices. 2nd ed. Zbl 1301.60002
Bai, Zhidong; Silverstein, Jack W.
2010
Probability inequalities. Zbl 1221.60001
Lin, Zhengyan; Bai, Zhidong
2010
On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Zbl 1373.62245
Bai, Zhidong; Chen, Jiaqi; Yao, Jianfeng
2010
Functional CLT for sample covariance matrices. Zbl 1210.60025
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2010
Analysis of rounded data from dependent sequences. Zbl 1432.62065
Zhang, Baoxue; Liu, Tianqing; Bai, Z. D.
2010
Rank regression for analysis of clustered data: a natural induced smoothing approach. Zbl 1464.62074
Fu, Liya; Wang, You-Gan; Bai, Zhidong
2010
The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix. Zbl 1200.15020
Bai, Z. D.; Zhang, L. X.
2010
Multivariate linear and nonlinear causality tests. Zbl 1201.62072
Bai, Zhidong; Wong, Wing-Keung; Zhang, Bingzhi
2010
Revisit of Sheppard corrections in linear regression. Zbl 1207.62123
Liu, TianQing; Zhang, BaoXue; Hu, GuoRong; Bai, ZhiDong
2010
Corrections to LRT on large-dimensional covariance matrix by RMT. Zbl 1360.62286
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2009
Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory. Zbl 1185.91155
Bai, Zhidong; Liu, Huixia; Wong, Wing-Keung
2009
CLT for linear spectral statistics of Wigner matrices. Zbl 1188.15032
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2009
Statistical analysis for rounded data. Zbl 1162.62012
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2009
Random matrix theory and its applications. Multivariate statistics and wireless communications. Zbl 1176.15001
2009
Central limit theorems for eigenvalues in a spiked population model. Zbl 1274.62129
Bai, Zhidong; Yao, Jian-Feng
2008
Large sample covariance matrices without independence structures in columns. Zbl 1135.62009
Bai, Zhidong; Zhou, Wang
2008
Statistical analysis for rounded data. Zbl 1269.62035
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2008
On constrained M-estimation and its recursive analog in multivariate linear regression models. Zbl 1135.62045
Bai, Zhidong; Chen, Xiru; Wu, Yuehua
2008
On asymptotics of eigenvectors of large sample covariance matrix. Zbl 1162.15012
Bai, Z. D.; Miao, B. Q.; Pan, G. M.
2007
On limit theorem for the eigenvalues of product of two random matrices. Zbl 1108.15022
Bai, Z. D.; Miao, Baiqi; Jin, Baisuo
2007
Semicircle law for Hadamard products. Zbl 1139.15012
Bai, Z. D.; Zhang, L. X.
2007
On the signal-to-interference ratio of CDMA systems in wireless communications. Zbl 1133.94012
Bai, Z. D.; Silverstein, Jack W.
2007
Statistics with estimated parameters. Zbl 1128.62026
Yang, Z. L.; Tse, Y. K.; Bai, Z. D.
2007
A generalized confidence interval for the difference of the means of two normal populations. Zbl 1133.62018
Tao, Jian; Biswas, Atanu; Bai, Zhi-Dong
2007
Spectral analysis of large dimensional random matrices. Zbl 1196.60002
Bai, Zhidong; Silverstein, Jack W.
2006
Rooted edges of a minimal directed spanning tree on random points. Zbl 1094.60004
Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.
2006
Asymptotics in randomized urn models. Zbl 1059.62111
Bai, Zhi-Dong; Hu, Feifang
2005
On the convergence of the spectral empirical process of Wigner matrices. Zbl 1101.60012
Bai, Z. D.; Yao, J.
2005
Maxima in hypercubes. Zbl 1080.60007
Bai, Zhi-Dong; Devroye, Luc; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2005
The broken sample problem. Zbl 1062.62041
Bai, Zhidong; Hsing, Tailen
2005
CLT for linear spectral statistics of large-dimensional sample covariance matrices. Zbl 1063.60022
Bai, Z. D.; Silverstein, Jack W.
2004
Ranked set sampling. Theory and applications. Zbl 1045.62007
Chen, Zehua; Bai, Zhidong; Sinha, Bimal K.
2004
A chi-square test for dimensionality with non-Gaussian data. Zbl 1032.62054
Bai, Z. D.; He, Xuming
2004
Convergence rates of spectral distributions of large sample covariance matrices. Zbl 1059.60036
Bai, Z. D.; Miao, Baiqi; Yao, Jian-feng
2003
An efficient algorithm for estimating the parameters of superimposed exponential signals. Zbl 1030.62062
Bai, Z. D.; Rao, C. R.; Chow, M.; Kundu, D.
2003
On the theory of ranked-set sampling and its ramifications. Zbl 1008.62023
Bai, Zhidong; Chen, Zehua
2003
Berry-{E}sseen bounds for the number of maxima in planar regions. Zbl 1065.60020
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2003
Weighted $$W$$ test for normality and asymptotics a revisit of Chen–Shapiro test for normality. Zbl 1026.62042
Bai, Z. D.; Chen, Ling
2003
Convergence rate of the best-$$r$$-point-average estimator for the maximizer of a nonparametric regression function. Zbl 1140.62320
Bai, Zhidong; Chen, Zehua; Wu, Yaohua
2003
Asymptotic properties of adaptive designs for clinical trials with delayed response. Zbl 1012.62087
Bai, Z. D.; Hu, Feifang; Rosenberger, William F.
2002
Gaussian approximation theorems for urn models and their applications. Zbl 1014.60025
Bai, Z. D.; Hu, Feifang; Zhang, Li-Xin
2002
Convergence rates of the spectral distributions of large Wigner matrices. Zbl 0987.60050
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
2002
...and 85 more Documents
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### Cited by 2,330 Authors

 99 Bai, Zhi-Dong 34 Pan, Guangming 33 Yao, Jianfeng 29 Bose, Arup 26 Zhou, Wang 25 Götze, Friedrich 25 Zheng, Shurong 23 Erdős, László 23 Hu, Jiang 22 Jiang, Tiefeng 21 Hu, Feifang 20 Silverstein, Jack W. 20 Tikhomirov, Alexander Nikolaevich 20 Zhang, Li-Xin 19 Aoshima, Makoto 19 Yata, Kazuyoshi 18 Vu, Van H. 17 Li, Weiming 17 Wu, Yuehua 16 Fujikoshi, Yasunori 15 Sung, Soohak 15 Wong, Wing-Keung 15 Yin, Yanqing 15 Zhao, Lincheng 14 Chen, Pingyan 14 Cui, Hengjian 14 O’Rourke, Sean D. 13 Bordenave, Charles 13 Péché, Sandrine 13 Zhang, Jinting 12 Chafaï, Djalil 12 El Karoui, Noureddine 12 Kundu, Debasis 12 Miao, Bai-qi 12 Soshnikov, Alexander B. 12 Wang, Xuejun 11 Bao, Zhigang 11 Bodnar, Taras 11 Couillet, Romain 11 Jiang, Dandan 11 Jin, Baisuo 11 Krüger, Torben 11 Najim, Jamal 11 Tao, Terence 10 Benaych-Georges, Florent 10 Guionnet, Alice 10 Jafari Jozani, Mohammad 10 Ledoit, Olivier 10 Modarres, Reza 10 Qi, Yongcheng 10 Tikhomirov, Konstantin E. 10 Yin, Jun 10 Zou, Changliang 9 Baik, Jinho 9 Capitaine, Mireille 9 Hachem, Walid 9 Heiny, Johannes 9 Li, Runze 9 Litvak, Aleksandr Evgen’evich 9 Rao, Calyampudi Radhakrishna 9 Renfrew, David 9 Rudelson, Mark 9 Saha, Koushik 9 Shen, Aiting 9 Vershynin, Roman 9 Wolf, Michael 9 Xie, Junshan 9 Zuo, Yijun 8 Adamczak, Radosław 8 Balakrishnan, Narayanaswamy 8 Basak, Anirban 8 Dette, Holger 8 Ding, Xue 8 Dobriban, Edgar 8 Feng, Long 8 Harrar, Solomon W. 8 Hazra, Rajat Subhra 8 Johnstone, Iain Murray 8 Lachos Dávila, Víctor Hugo 8 Lin, Zhengyan 8 Liu, Baisen 8 Lytova, Anna 8 Naumov, Alekseĭ Aleksandrovich 8 Nechita, Ion 8 Parolya, Nestor R. 8 Paul, Debashis 8 Rousseeuw, Peter J. 8 Tomczak-Jaegermann, Nicole 8 Wang, Chen 8 Wang, Cheng 8 Wu, Yaohua 8 Yau, Horng-Tzer 8 Zhu, Lixing 7 Chen, Songxi 7 Ding, Xiucai 7 Fan, Jianqing 7 Guo, Jia 7 He, Xuming 7 Hyodo, Masashi 7 Ishii, Aki ...and 2,230 more Authors
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### Cited in 290 Serials

 191 Journal of Multivariate Analysis 135 The Annals of Statistics 90 Random Matrices: Theory and Applications 87 Journal of Statistical Planning and Inference 86 Statistics & Probability Letters 69 Communications in Statistics. Theory and Methods 66 Computational Statistics and Data Analysis 56 Journal of Theoretical Probability 51 The Annals of Probability 51 Probability Theory and Related Fields 41 Bernoulli 37 The Annals of Applied Probability 32 Journal of Statistical Physics 32 Annals of the Institute of Statistical Mathematics 31 Statistical Papers 31 Electronic Journal of Statistics 29 Journal of Mathematical Physics 29 Journal of Statistical Computation and Simulation 23 Stochastic Processes and their Applications 23 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 19 Communications in Mathematical Physics 19 Journal of Econometrics 19 Computational Statistics 19 Communications in Statistics. Simulation and Computation 19 Electronic Journal of Probability 18 Statistics 16 Advances in Applied Probability 16 Metrika 16 Test 16 Statistica Sinica 15 Journal of Inequalities and Applications 15 Journal of the Korean Statistical Society 15 Science China. Mathematics 14 Acta Mathematicae Applicatae Sinica. English Series 14 Science in China. Series A 13 Linear Algebra and its Applications 13 Acta Mathematica Sinica. English Series 12 Advances in Mathematics 12 Journal of Applied Probability 12 Journal of Nonparametric Statistics 11 Journal of Mathematical Analysis and Applications 11 Journal of the American Statistical Association 11 Journal of Functional Analysis 11 Australian & New Zealand Journal of Statistics 9 Journal of Machine Learning Research (JMLR) 8 Scandinavian Journal of Statistics 8 Theory of Probability and its Applications 8 Journal of Mathematical Sciences (New York) 8 Journal of Applied Statistics 7 Biometrics 7 Random Structures & Algorithms 7 Methodology and Computing in Applied Probability 6 Communications on Pure and Applied Mathematics 6 Sequential Analysis 6 Statistical Science 6 European Journal of Operational Research 6 Filomat 6 Annales Henri Poincaré 6 Brazilian Journal of Probability and Statistics 6 Statistical Methodology 6 Journal of Statistical Theory and Practice 6 Sankhyā. Series A 5 Lithuanian Mathematical Journal 5 Proceedings of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Journal of Time Series Analysis 5 Applied Mathematics. Series B (English Edition) 5 Mathematical Problems in Engineering 5 Journal of Systems Science and Complexity 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 AStA. Advances in Statistical Analysis 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 The Canadian Journal of Statistics 4 Indian Journal of Pure & Applied Mathematics 4 Israel Journal of Mathematics 4 Econometric Reviews 4 Geometric and Functional Analysis. GAFA 4 Abstract and Applied Analysis 4 Journal of the Royal Statistical Society. Series B. Statistical Methodology 4 Discrete Dynamics in Nature and Society 4 Econometric Theory 4 Journal of Applied Mathematics 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 4 Advances in Data Analysis and Classification. ADAC 4 The Annals of Applied Statistics 3 Physica A 3 Applied Mathematics and Computation 3 Acta Mathematica Hungarica 3 Bulletin of the American Mathematical Society. New Series 3 Applied and Computational Harmonic Analysis 3 Mathematical Methods of Statistics 3 Combinatorics, Probability and Computing 3 Electronic Communications in Probability 3 Doklady Mathematics 3 Statistical Inference for Stochastic Processes 3 Journal of the European Mathematical Society (JEMS) 3 Quantitative Finance 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Hacettepe Journal of Mathematics and Statistics 3 Statistical Methods and Applications ...and 190 more Serials
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### Cited in 46 Fields

 1,324 Statistics (62-XX) 991 Probability theory and stochastic processes (60-XX) 502 Linear and multilinear algebra; matrix theory (15-XX) 150 Numerical analysis (65-XX) 82 Combinatorics (05-XX) 74 Statistical mechanics, structure of matter (82-XX) 73 Functional analysis (46-XX) 52 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 46 Computer science (68-XX) 35 Information and communication theory, circuits (94-XX) 32 Biology and other natural sciences (92-XX) 31 Quantum theory (81-XX) 30 Operator theory (47-XX) 27 Operations research, mathematical programming (90-XX) 18 Dynamical systems and ergodic theory (37-XX) 12 Special functions (33-XX) 12 Convex and discrete geometry (52-XX) 12 Systems theory; control (93-XX) 9 Partial differential equations (35-XX) 9 Approximations and expansions (41-XX) 8 Number theory (11-XX) 7 Ordinary differential equations (34-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Integral transforms, operational calculus (44-XX) 4 Group theory and generalizations (20-XX) 4 Functions of a complex variable (30-XX) 3 Real functions (26-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX)