Hu, Shuhe

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 Author ID: hu.shuhe Published as: Hu, Shuhe; Hu, Shu He; Hu, Shu-he; Hu, S. H.; Hu, S.; Hu, ShuHe more...less External Links: ORCID · Math-Net.Ru · dblp
 Documents Indexed: 202 Publications since 1986 Co-Authors: 80 Co-Authors with 168 Joint Publications 2,786 Co-Co-Authors
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Co-Authors

 30 single-authored 107 Wang, Xuejun 67 Yang, Wenzhi 24 Wang, Xinghui 20 Li, Xiaoqin 19 Shen, Yan 12 Wu, Yi 6 Chen, Guijing 6 Ling, Nengxiang 6 Volodin, Andrei I. 5 Zhou, Xingcai 4 Chen, Zhiyong 4 Deng, Xin 4 Shen, Aiting 4 Zhao, Ting 3 Hong, Shengyan 3 Ling, Jimin 3 Liu, Tingting 3 Pan, Guangming 3 Wang, Shijie 3 Wang, Yiwei 3 Xu, Chen 3 Zhao, Zhangrui 2 Chen, Minghua 2 Cheng, Yebin 2 Ge, Meimei 2 Han, Ruidong 2 Hu, Ming 2 Hu, Tienchung 2 Liu, Xiaotao 2 Ma, Songlin 2 Prakasa Rao, B. L. S. 2 Ren, Zhe 2 Wei, Yunfei 2 Xi, Mengmei 2 Xia, Fengxi 2 Yang, Lei 2 Zhang, Qinchi 2 Zhang, Yongjun 2 Zheng, Lulu 1 Chen, Enbing 1 Chen, Ling 1 Chen, Zhuqiang 1 Cheng, Zhengdong 1 Dai, Pingping 1 Fang, Hong 1 Fang, Libao 1 Gao, Qibing 1 He, Zehui 1 Hu, Xiaopeng 1 Li, Bainian 1 Li, Xu 1 Li, Zhenglong 1 Lin, Jinguan 1 Liu, Xi 1 Liu, Xinsheng 1 Mei, Men Chang 1 Qiao, Xudong 1 Ren, Chunguang 1 Shi, Xiaoping 1 Sun, Jiaguang 1 Tan, Xing-Yu 1 Tang, Xufei 1 Wang, Haibin 1 Wang, Hongrui 1 Wang, Hongxia 1 Wang, Huilong 1 Wang, Lichun 1 Wang, Xize 1 Wei, Da 1 Wei, Yongli 1 Wu, Tao 1 Xiong, Huailu 1 Xu, Haiyun 1 Yang, Lianqiang 1 Yang, Yingying 1 Yong, Junhai 1 Yu, Wei 1 Zha, Tingting 1 Zhang, Yanhua 1 Zhang, Yuanyuan 1 Zhang, Zhimian 1 Zhou, Weixin 1 Zhu, Chunhua
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Serials

 14 Journal of Inequalities and Applications 12 Statistics & Probability Letters 11 Communications in Statistics. Theory and Methods 6 Acta Mathematica Sinica 6 Chinese Journal of Applied Probability and Statistics 6 Abstract and Applied Analysis 5 Metrika 5 Acta Mathematicae Applicatae Sinica 5 Statistics 5 Test 5 Statistical Papers 5 Discrete Dynamics in Nature and Society 4 Journal of Mathematical Analysis and Applications 4 Journal of Systems Science and Mathematical Sciences 4 Mathematica Applicata 4 Applied Mathematics. Series A (Chinese Edition) 4 Acta Mathematica Scientia. Series A. (Chinese Edition) 4 Stochastics 3 Chinese Annals of Mathematics. Series A 3 Acta Mathematicae Applicatae Sinica. English Series 3 Applied Mathematics Letters 3 Systems Science and Mathematical Sciences 3 Chinese Science Bulletin 3 Chinese Quarterly Journal of Mathematics 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Journal of University of Science and Technology of China 3 Journal of Hefei University of Technology. Natural Science 3 Journal of Anhui University. Natural Science Edition 3 Communications in Mathematical Research 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Theory of Probability and its Applications 2 Journal of Statistical Planning and Inference 2 Journal of Mathematics. Wuhan University 2 Stochastic Analysis and Applications 2 Northeastern Mathematical Journal 2 Science in China. Series A 2 Applied Mathematics. Series B (English Edition) 2 Filomat 2 Pure and Applied Mathematics 2 Journal of Nonparametric Statistics 2 Acta Mathematica Sinica. English Series 2 Probability in the Engineering and Informational Sciences 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 Journal of the Korean Statistical Society 2 Journal of Mathematical Inequalities 2 Journal of Mathematical Research with Applications 1 Acta Mechanica 1 Analysis Mathematica 1 Annals of the Institute of Statistical Mathematics 1 Kybernetika 1 Journal of Mathematical Research & Exposition 1 Bulletin of the Korean Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Journal of Northeast Normal University. Natural Science Edition 1 Computer Aided Geometric Design 1 Journal of Engineering Mathematics (Xi’an) 1 Journal of Theoretical Probability 1 Mechanical Systems and Signal Processing 1 Applications of Mathematics 1 Acta Mathematica Sinica. New Series 1 Applied Mathematics 1 Journal of Anhui Normal University. Natural Science 1 Mathematical Inequalities & Applications 1 Australian & New Zealand Journal of Statistics 1 Journal of Mathematical Study 1 Statistical Methods and Applications 1 MASA. Model Assisted Statistics and Applications 1 Frontiers of Mathematics in China 1 AStA. Advances in Statistical Analysis 1 Electronic Journal of Statistics 1 Chinese Journal of Engineering Mathematics
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Fields

 130 Probability theory and stochastic processes (60-XX) 104 Statistics (62-XX) 2 Approximations and expansions (41-XX) 1 Number theory (11-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Citations contained in zbMATH Open

126 Publications have been cited 1,249 times in 438 Documents Cited by Year
On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. Zbl 1307.60024
Wang, Xuejun; Xu, Chen; Hu, Tien-Chung; Volodin, Andrei; Hu, Shuhe
2014
Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Zbl 1319.60063
Wang, Xuejun; Deng, Xin; Zheng, Lulu; Hu, Shuhe
2014
Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors. Zbl 1367.62152
Wang, Xuejun; Zheng, Lulu; Xu, Chen; Hu, Shuhe
2015
Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. Zbl 1316.60042
Wang, Xuejun; Shen, Aiting; Chen, Zhiyong; Hu, Shuhe
2015
Complete convergence and complete moment convergence for martingale difference sequence. Zbl 1285.60031
Wang, Xue Jun; Hu, Shu He
2014
Complete consistency of estimators for regression models based on extended negatively dependent errors. Zbl 1401.62074
Yang, Wenzhi; Xu, Haiyun; Chen, Ling; Hu, Shuhe
2018
Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Zbl 1263.60025
Shen, Yan; Wang, Xuejun; Yang, Wenzhi; Hu, Shuhe
2013
Exponential inequalities and inverse moment for NOD sequence. Zbl 1186.60015
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Ling, Nengxiang
2010
Fixed-design regression for linear time series. Zbl 1010.62085
Hu, Shuhe; Zhu, Chunhua; Chen, Yebin; Wang, Lichun
2002
Complete convergence for arrays of rowwise negatively orthant dependent random variables. Zbl 1260.60062
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2012
Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model. Zbl 1378.60063
Wu, Yi; Wang, Xuejun; Hu, Shuhe
2017
Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables. Zbl 1276.60036
Wang, Xuejun; Hu, Tien-Chung; Volodin, Andrei; Hu, Shuhe
2013
On complete convergence for an extended negatively dependent sequence. Zbl 1300.60038
Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe; Wang, Xinghui
2014
The consistency of the nearest neighbor estimator of the density function based on WOD samples. Zbl 1325.62085
Wang, Xuejun; Hu, Shuhe
2015
Berry-Esséen bound of sample quantiles for $$\varphi$$-mixing random variables. Zbl 1232.60020
Yang, Wenzhi; Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe
2012
On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables. Zbl 1290.60040
Wang, Xuejun; Wang, Shijie; Hu, Shuhe; Ling, Jimin; Wei, Yunfei
2013
On complete convergence for arrays of rowwise weakly dependent random variables. Zbl 1251.60025
Wang, Xuejun; Li, Xiaoqin; Yang, Wenzhi; Hu, Shuhe
2012
On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Zbl 1474.62159
Yang, Wenzhi; Liu, Tingting; Wang, Xuejun; Hu, Shuhe
2014
The consistency for estimator of nonparametric regression model based on NOD errors. Zbl 1294.62072
Yang, Wenzhi; Wang, Xuejun; Wang, Xinghui; Hu, Shuhe
2012
On extending the Brunk-Prokhorov strong law of large numbers for martingale differences. Zbl 1152.60317
Hu, Shuhe; Chen, Guijing; Wang, Xuejun
2008
Strong limit theorems for weighted sums of NOD sequence and exponential inequalities. Zbl 1234.60035
Wang, Xuejun; Hu, Shuhe; Volodin, Andrei I.
2011
Fixed-design semiparametric regression for linear time series. Zbl 1092.62047
Hu, Shuhe
2006
An exponential inequality for a NOD sequence and a strong law of large numbers. Zbl 1205.60068
Wang, Xuejun; Hu, Shuhe; Shen, Aiting; Yang, Wenzhi
2011
On complete convergence for weighted sums of $$\varphi$$-mixing random variables. Zbl 1208.60031
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Shen, Yan
2010
Exponential inequalities and complete convergence for a LNQD sequence. Zbl 1294.60037
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Li, Xiaoqin
2010
Convergence properties for asymptotically almost negatively associated sequence. Zbl 1207.60025
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2010
Strong limit theorems for weighted sums of negatively associated random variables. Zbl 1208.60028
Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe; Yang, Wenzhi
2011
Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors. Zbl 1421.62023
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2018
Complete moment convergence for double-indexed randomly weighted sums and its applications. Zbl 1391.60055
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2018
Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables. Zbl 1235.60026
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2011
The Bahadur representation for sample quantiles under strongly mixing sequence. Zbl 1209.62116
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2011
On complete convergence of moving average process for AANA sequence. Zbl 1247.60043
Yang, Wenzhi; Wang, Xuejun; Ling, Nengxiang; Hu, Shuhe
2012
The Berry-Esséen type bound of sample quantiles for strong mixing sequence. Zbl 1227.62008
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun; Ling, Nengxiang
2012
The Bahadur representation for sample quantile under NOD sequence. Zbl 1359.62156
Li, Xiaoqin; Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
2011
Some Baum-Katz type results for $${\varphi}$$-mixing random variables with different distributions. Zbl 1266.60056
Wang, Xuejun; Hu, Shuhe
2012
Exponential probability inequality for $$m$$-END random variables and its applications. Zbl 1330.60031
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2016
On complete convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables. Zbl 1253.60044
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui
2012
Estimation problem of regression model with linear process errors. Zbl 1020.62055
Hu, Shuhe; Pan, Guangming; Gao, Qibing
2003
Mean consistency for a semiparametric regression model. Zbl 1052.62043
Pan, Guangming; Hu, Shuhe; Fang, Libao; Cheng, Zhengdong
2003
Large deviations for some dependent sequences. Zbl 1174.60007
Hu, Shuhe; Wang, Xuejun
2008
A general approach rate to the strong law of large numbers. Zbl 1090.60030
Hu, Shuhe; Hu, Ming
2006
Weighted version of strong law of large numbers for a class of random variables and its applications. Zbl 1402.60037
Wu, Yi; Wang, Xuejun; Hu, Shuhe; Yang, Lianqiang
2018
Weak laws of large numbers for arrays of dependent random variables. Zbl 1337.60028
Wang, Xinghui; Hu, Shuhe
2014
A note on the Berry-Esseen bound of sample quantiles for $$\varphi$$-mixing sequence. Zbl 1305.62116
Yang, Wenzhi; Wang, Xuejun; Hu, Shuhe
2014
Large deviation for a least squares estimator in a nonlinear regression model. Zbl 1288.62034
Yang, Wenzhi; Hu, Shuhe
2014
On Bahadur representation for sample quantiles under $$\alpha$$-mixing sequence. Zbl 1297.62054
Zhang, Qinchi; Yang, Wenzhi; Hu, Shuhe
2014
Consistency estimate for a new semiparametric regression model. Zbl 0905.62035
Hu, Shuhe
1997
Doob’s type inequality and strong law of large numbers for demimartingales. Zbl 1197.60021
Wang, Xuejun; Hu, Shuhe; Zhao, Ting; Yang, Wenzhi
2010
Estimate for a semiparametric regression model. Zbl 0954.62050
Hu, Shuhe
1999
On inverse moments of nonnegative weakly convergent random variables. Zbl 1141.60309
Hu, Shuhe; Chen, Guijing; Wang, Xuejun; Chen, Enbing
2007
The Hàjek-Rènyi-type inequality for associated random variables. Zbl 1159.60310
Hu, Shuhe; Wang, Xuejun; Yang, Wenzhi; Zhao, Ting
2009
Maximal inequality for $$\psi$$-mixing sequences and its applications. Zbl 1197.60031
Wang, Xuejun; Hu, Shuhe; Shen, Yan; Yang, Wenzhi
2010
Maximal inequalities for demimartingales and their applications. Zbl 1198.60016
Wang, XueJun; Hu, ShuHe
2009
The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors. Zbl 1054.62076
Hu, Shuhe
2002
The tail probability of the product of dependent random variables from max-domains of attraction. Zbl 1227.60018
Yang, Yingying; Hu, Shuhe; Wu, Tao
2011
Comments on the paper: A bilateral inequality on the Borel-Cantelli Lemma. Zbl 1170.60311
Hu, Shuhe; Wang, Xuejun; Li, Xiaoqin; Zhang, Yuanyuan
2009
Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables. Zbl 1310.60024
Chen, Zhiyong; Wang, Xuejun; Hu, Shuhe
2015
Complete moment convergence for randomly weighted sums of martingale differences. Zbl 1295.60056
Yang, Wenzhi; Wang, Yiwei; Wang, Xinghui; Hu, Shuhe
2013
On the strong convergence and some inequalities for negatively superadditive dependent sequences. Zbl 1294.60054
Shen, Yan; Wang, Xuejun; Hu, Shuhe
2013
The consistency for the estimators of semiparametric regression model based on weakly dependent errors. Zbl 1370.62026
Wang, Xuejun; Deng, Xin; Xia, Fengxi; Hu, Shuhe
2017
Degree reduction of B-spline curves. Zbl 0971.68169
Yong, J.-H.; Hu, S.-H.; Sun, J.-G.; Tan, Xing-Yu
2001
Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences. Zbl 1266.60035
Yang, Wenzhi; Shen, Yan; Hu, Shuhe; Wang, Xuejun
2012
Maximal inequalities for some dependent sequences and their applications. Zbl 1296.60041
Hu, Shuhe; Li, Xiaoqin; Yang, Wenzhi; Wang, Xuejun
2011
On consistency of least square estimators in the simple linear EV model with negatively orthant dependent errors. Zbl 1362.62051
Wang, Xuejun; Hu, Shuhe
2017
Maximal inequalities for $$N$$-demimartingale and strong law of large numbers. Zbl 1223.60019
Wang, Xuejun; Hu, Shuhe; Prakasa Rao, B. L. S.; Yang, Wenzhi
2011
Complete convergence for arrays of row-wise negatively superadditive-dependent random variables and its applications. Zbl 1374.60056
Wu, Yi; Wang, Xuejun; Hu, Shuhe
2016
Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models. Zbl 1447.60057
Wang, Xuejun; Wu, Yi; Hu, Shuhe; Ling, Nengxiang
2020
Some new results for the strong law of large numbers. Zbl 1039.60026
Hu, Shuhe
2003
The Berry-Esseen bounds of the weighted estimator in a nonparametric regression model. Zbl 1431.62173
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2019
On consistency of the weighted least squares estimators in a semiparametric regression model. Zbl 1401.62066
Wang, Xuejun; Deng, Xin; Hu, Shuhe
2018
The Bahadur representation of sample quantiles for weakly dependent sequences. Zbl 1341.62085
Wang, Yiwei; Yang, Wenzhi; Hu, Shuhe
2016
Complete convergence of weighted sums for arrays of rowwise $$\varphi$$-mixing random variables. Zbl 1340.60045
Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe
2014
Complete moment convergence of pairwise NQD random variables. Zbl 1320.60086
Yang, Wenzhi; Hu, Shuhe
2015
A note on the inverse moment for the non negative random variables. Zbl 1294.60034
Hu, Shuhe; Wang, Xinghui; Yang, Wenzhi; Wang, Xuejun
2014
On some maximal inequalities for demimartingales and $$N$$-demimartingales based on concave Young functions. Zbl 1290.60049
Wang, Xuejun; Prakasa Rao, B. L. S.; Hu, Shuhe; Yang, Wenzhi
2012
Strong law of large numbers and growth rate for a class of random variable sequences. Zbl 1153.60018
Wang, Xuejun; Hu, Shuhe; Shen, Yan; Ling, Nengxiang
2008
A general result on complete convergence for weighted sums of linear processes and its statistical applications. Zbl 1418.62073
Deng, Xin; Wang, Xuejun; Hu, Shuhe; Hu, Ming
2019
General results of complete convergence and complete moment convergence for weighted sums of some class of random variables. Zbl 1346.60034
Wang, Xuejun; Hu, Shuhe; Volodin, Andrei
2016
On the strong consistency of M-estimates in linear models for negatively superadditive dependent errors. Zbl 1336.62094
Wang, Xinghui; Hu, Shuhe
2015
Complete consistency of the estimator of nonparametric regression models based on $$\tilde{\rho}$$-mixing sequences. Zbl 1256.62021
Wang, Xuejun; Xia, Fengxi; Ge, Meimei; Hu, Shuhe; Yang, Wenzhi
2012
Some inequalities for demimartingales and $$N$$-demimartingales. Zbl 1241.60012
Hu, Shuhe; Wang, Xinghui; Yang, Wenzhi; Wang, Xuejun
2012
Convergence rates in the strong law of large numbers for martingale difference sequences. Zbl 1253.60045
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui
2012
The Berry-Esseen bounds for kernel density estimator under dependent sample. Zbl 1283.62080
Yang, Wenzhi; Hu, Shuhe
2012
Complete convergence for moving average process of martingale differences. Zbl 1261.60038
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
2012
Analytical solutions of thermal buckling and postbuckling of symmetric laminated composite beams with various boundary conditions. Zbl 1401.74099
Fu, Y.; Wang, J.; Hu, S.
2014
Moment consistency of estimators in partially linear models under NA samples. Zbl 1197.62064
Zhou, Xingcai; Liu, Xinsheng; Hu, Shuhe
2010
A note on the inequalities for $$N$$-demimartingales and demimartingales. Zbl 1240.60027
Hu, Shuhe; Yang, Wenzhi; Wang, Xuejun; Shen, Yan
2010
Asymptotics for the linear kernel quantile estimator. Zbl 1439.62119
Wang, Xuejun; Wu, Yi; Yu, Wei; Yang, Wenzhi; Hu, Shuhe
2019
Moment inequalities for $$m$$-NOD random variables and their applications. Zbl 1405.60027
Wang, X. J.; Hu, S. H.; Volodin, A. I.
2018
The inverse moment for widely orthant dependent random variables. Zbl 1376.60045
Li, Xiaoqin; Liu, Xi; Yang, Wenzhi; Hu, Shuhe
2016
Berry-Esséen bound of sample quantiles for negatively associated sequence. Zbl 1395.62106
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun; Zhang, Qinchi
2011
On strong law of large numbers and growth rate for a class of random variables. Zbl 1291.60059
Shen, Yan; Yang, Jie; Hu, Shuhe
2013
Moment consistency of estimators in a semi-parametric regression model under NA samples. Zbl 1223.62058
Zhou, Xingcai; Hu, Shuhe
2010
Central limit theorem for the weighted sum of a martingale difference. Zbl 0990.60018
Hu, Shuhe
2001
Strong consistency of a class of estimators in a partial linear model. Zbl 1103.62338
Chen, Minghua; Ren, Zhe; Hu, Shuhe
1998
The large deviation results for the nonlinear regression model with dependent errors. Zbl 06833480
Yang, Wenzhi; Zhao, Zhangrui; Wang, Xinghui; Hu, Shuhe
2017
Some new results for weakly dependent random variable sequences. Zbl 1240.60085
Wang, Xuejun; Hu, Shuhe; Shen, Yan; Yang, Wenzhi
2010
Berry-Esseen type bounds of the estimators in a semiparametric model under linear process errors with $$\alpha$$-mixing dependent innovations. Zbl 1423.62025
Wu, Yi; Wang, Xuejun; Li, Yongming; Hu, Shuhe
2019
The Berry-Esséen bound of sample quantiles for NA sequence. Zbl 1373.62209
Liu, Tingting; Zhang, Zhimian; Hu, Shuhe; Yang, Wenzhi
2014
Extensions of the Borel-Cantelli lemma in general measure spaces. Zbl 1362.60014
Wang, Xuejun; Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe
2014
Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models. Zbl 1447.60057
Wang, Xuejun; Wu, Yi; Hu, Shuhe; Ling, Nengxiang
2020
The Berry-Esseen bounds of the weighted estimator in a nonparametric regression model. Zbl 1431.62173
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2019
A general result on complete convergence for weighted sums of linear processes and its statistical applications. Zbl 1418.62073
Deng, Xin; Wang, Xuejun; Hu, Shuhe; Hu, Ming
2019
Asymptotics for the linear kernel quantile estimator. Zbl 1439.62119
Wang, Xuejun; Wu, Yi; Yu, Wei; Yang, Wenzhi; Hu, Shuhe
2019
Berry-Esseen type bounds of the estimators in a semiparametric model under linear process errors with $$\alpha$$-mixing dependent innovations. Zbl 1423.62025
Wu, Yi; Wang, Xuejun; Li, Yongming; Hu, Shuhe
2019
The Berry-Esseen bound for $$\rho$$-mixing random variables and its applications in nonparametric regression model. Zbl 1411.62108
Wang, X. J.; Hu, S. H.
2019
The Bahadur representation for sample quantiles under dependent sequence. Zbl 1432.62122
Yang, Wen-zhi; Hu, Shu-he; Wang, Xue-jun
2019
The laws of large numbers for Pareto-type random variables with infinite means. Zbl 07539694
Yang, Wenzhi; Yang, Lei; Wei, Da; Hu, Shuhe
2019
Complete consistency of estimators for regression models based on extended negatively dependent errors. Zbl 1401.62074
Yang, Wenzhi; Xu, Haiyun; Chen, Ling; Hu, Shuhe
2018
Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors. Zbl 1421.62023
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2018
Complete moment convergence for double-indexed randomly weighted sums and its applications. Zbl 1391.60055
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2018
Weighted version of strong law of large numbers for a class of random variables and its applications. Zbl 1402.60037
Wu, Yi; Wang, Xuejun; Hu, Shuhe; Yang, Lianqiang
2018
On consistency of the weighted least squares estimators in a semiparametric regression model. Zbl 1401.62066
Wang, Xuejun; Deng, Xin; Hu, Shuhe
2018
Moment inequalities for $$m$$-NOD random variables and their applications. Zbl 1405.60027
Wang, X. J.; Hu, S. H.; Volodin, A. I.
2018
Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model. Zbl 1378.60063
Wu, Yi; Wang, Xuejun; Hu, Shuhe
2017
The consistency for the estimators of semiparametric regression model based on weakly dependent errors. Zbl 1370.62026
Wang, Xuejun; Deng, Xin; Xia, Fengxi; Hu, Shuhe
2017
On consistency of least square estimators in the simple linear EV model with negatively orthant dependent errors. Zbl 1362.62051
Wang, Xuejun; Hu, Shuhe
2017
The large deviation results for the nonlinear regression model with dependent errors. Zbl 06833480
Yang, Wenzhi; Zhao, Zhangrui; Wang, Xinghui; Hu, Shuhe
2017
Some probability inequalities of least-squares estimator in non linear regression model with strong mixing errors. Zbl 1360.62376
Yang, Wenzhi; Wang, Yiwei; Hu, Shuhe
2017
Complete convergence of randomly weighted sums of NOD random variables. Zbl 1399.60065
Zhao, Zhangrui; Qiao, Xudong; Yang, Wenzhi; Hu, Shuhe
2017
The inequalities of randomly weighted sums of pairwise NQD sequences and its application to limit theory. Zbl 1369.60018
Li, Xiaoqin; Zhao, Zhangrui; Yang, Wenzhi; Hu, Shuhe
2017
The strong consistency of $$M$$-estimates in linear models with extended negatively dependent errors. Zbl 1369.62046
Wang, Xinghui; Hu, Shuhe
2017
Asymptotics of self-weighted M-estimators for autoregressive models. Zbl 1365.62349
Wang, Xinghui; Hu, Shuhe
2017
On the asymptotic approximation of inverse moment for non negative random variables. Zbl 1386.60080
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
2017
Exponential probability inequality for $$m$$-END random variables and its applications. Zbl 1330.60031
Wang, Xuejun; Wu, Yi; Hu, Shuhe
2016
Complete convergence for arrays of row-wise negatively superadditive-dependent random variables and its applications. Zbl 1374.60056
Wu, Yi; Wang, Xuejun; Hu, Shuhe
2016
The Bahadur representation of sample quantiles for weakly dependent sequences. Zbl 1341.62085
Wang, Yiwei; Yang, Wenzhi; Hu, Shuhe
2016
General results of complete convergence and complete moment convergence for weighted sums of some class of random variables. Zbl 1346.60034
Wang, Xuejun; Hu, Shuhe; Volodin, Andrei
2016
The inverse moment for widely orthant dependent random variables. Zbl 1376.60045
Li, Xiaoqin; Liu, Xi; Yang, Wenzhi; Hu, Shuhe
2016
On the exponential inequalities for widely orthant-dependent random variables. Zbl 1375.60056
Liu, Tingting; Wang, Xuejun; Wang, Xinghui; Hu, Shuhe
2016
A note on the strong consistency of M-estimates in linear models. Zbl 1333.62077
Wang, Xinghui; Hu, Shuhe
2016
Uniform convergence of estimator for nonparametric regression with dependent data. Zbl 1337.62061
Li, Xiaoqin; Yang, Wenzhi; Hu, Shuhe
2016
Approximations to inverse moments of double-indexed weighted sums. Zbl 1381.60049
Yang, Wenzhi; Shi, Xiaoping; Li, Xiaoqin; Hu, Shuhe
2016
Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors. Zbl 1367.62152
Wang, Xuejun; Zheng, Lulu; Xu, Chen; Hu, Shuhe
2015
Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. Zbl 1316.60042
Wang, Xuejun; Shen, Aiting; Chen, Zhiyong; Hu, Shuhe
2015
The consistency of the nearest neighbor estimator of the density function based on WOD samples. Zbl 1325.62085
Wang, Xuejun; Hu, Shuhe
2015
Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables. Zbl 1310.60024
Chen, Zhiyong; Wang, Xuejun; Hu, Shuhe
2015
Complete moment convergence of pairwise NQD random variables. Zbl 1320.60086
Yang, Wenzhi; Hu, Shuhe
2015
On the strong consistency of M-estimates in linear models for negatively superadditive dependent errors. Zbl 1336.62094
Wang, Xinghui; Hu, Shuhe
2015
On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. Zbl 1307.60024
Wang, Xuejun; Xu, Chen; Hu, Tien-Chung; Volodin, Andrei; Hu, Shuhe
2014
Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Zbl 1319.60063
Wang, Xuejun; Deng, Xin; Zheng, Lulu; Hu, Shuhe
2014
Complete convergence and complete moment convergence for martingale difference sequence. Zbl 1285.60031
Wang, Xue Jun; Hu, Shu He
2014
On complete convergence for an extended negatively dependent sequence. Zbl 1300.60038
Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe; Wang, Xinghui
2014
On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Zbl 1474.62159
Yang, Wenzhi; Liu, Tingting; Wang, Xuejun; Hu, Shuhe
2014
Weak laws of large numbers for arrays of dependent random variables. Zbl 1337.60028
Wang, Xinghui; Hu, Shuhe
2014
A note on the Berry-Esseen bound of sample quantiles for $$\varphi$$-mixing sequence. Zbl 1305.62116
Yang, Wenzhi; Wang, Xuejun; Hu, Shuhe
2014
Large deviation for a least squares estimator in a nonlinear regression model. Zbl 1288.62034
Yang, Wenzhi; Hu, Shuhe
2014
On Bahadur representation for sample quantiles under $$\alpha$$-mixing sequence. Zbl 1297.62054
Zhang, Qinchi; Yang, Wenzhi; Hu, Shuhe
2014
Complete convergence of weighted sums for arrays of rowwise $$\varphi$$-mixing random variables. Zbl 1340.60045
Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe
2014
A note on the inverse moment for the non negative random variables. Zbl 1294.60034
Hu, Shuhe; Wang, Xinghui; Yang, Wenzhi; Wang, Xuejun
2014
Analytical solutions of thermal buckling and postbuckling of symmetric laminated composite beams with various boundary conditions. Zbl 1401.74099
Fu, Y.; Wang, J.; Hu, S.
2014
The Berry-Esséen bound of sample quantiles for NA sequence. Zbl 1373.62209
Liu, Tingting; Zhang, Zhimian; Hu, Shuhe; Yang, Wenzhi
2014
Extensions of the Borel-Cantelli lemma in general measure spaces. Zbl 1362.60014
Wang, Xuejun; Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe
2014
The convergence of double-indexed weighted sums of martingale differences and its application. Zbl 1474.60116
Yang, Wenzhi; Wang, Xinghui; Li, Xiaoqin; Hu, Shuhe
2014
Some results for demimartingales and $$N$$-demimartingales. Zbl 1335.60014
Dai, Pingping; Shen, Yan; Hu, Shuhe; Yang, Wenzhi
2014
Some maximal type inequalities for $$N$$-demimartingales and related results. Zbl 1296.60049
Yang, Wenzhi; Hu, Shuhe
2014
Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Zbl 1263.60025
Shen, Yan; Wang, Xuejun; Yang, Wenzhi; Hu, Shuhe
2013
Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables. Zbl 1276.60036
Wang, Xuejun; Hu, Tien-Chung; Volodin, Andrei; Hu, Shuhe
2013
On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables. Zbl 1290.60040
Wang, Xuejun; Wang, Shijie; Hu, Shuhe; Ling, Jimin; Wei, Yunfei
2013
Complete moment convergence for randomly weighted sums of martingale differences. Zbl 1295.60056
Yang, Wenzhi; Wang, Yiwei; Wang, Xinghui; Hu, Shuhe
2013
On the strong convergence and some inequalities for negatively superadditive dependent sequences. Zbl 1294.60054
Shen, Yan; Wang, Xuejun; Hu, Shuhe
2013
On strong law of large numbers and growth rate for a class of random variables. Zbl 1291.60059
Shen, Yan; Yang, Jie; Hu, Shuhe
2013
Complete convergence for arrays of rowwise negatively orthant dependent random variables. Zbl 1260.60062
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2012
Berry-Esséen bound of sample quantiles for $$\varphi$$-mixing random variables. Zbl 1232.60020
Yang, Wenzhi; Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe
2012
On complete convergence for arrays of rowwise weakly dependent random variables. Zbl 1251.60025
Wang, Xuejun; Li, Xiaoqin; Yang, Wenzhi; Hu, Shuhe
2012
The consistency for estimator of nonparametric regression model based on NOD errors. Zbl 1294.62072
Yang, Wenzhi; Wang, Xuejun; Wang, Xinghui; Hu, Shuhe
2012
On complete convergence of moving average process for AANA sequence. Zbl 1247.60043
Yang, Wenzhi; Wang, Xuejun; Ling, Nengxiang; Hu, Shuhe
2012
The Berry-Esséen type bound of sample quantiles for strong mixing sequence. Zbl 1227.62008
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun; Ling, Nengxiang
2012
Some Baum-Katz type results for $${\varphi}$$-mixing random variables with different distributions. Zbl 1266.60056
Wang, Xuejun; Hu, Shuhe
2012
On complete convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables. Zbl 1253.60044
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui
2012
Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences. Zbl 1266.60035
Yang, Wenzhi; Shen, Yan; Hu, Shuhe; Wang, Xuejun
2012
On some maximal inequalities for demimartingales and $$N$$-demimartingales based on concave Young functions. Zbl 1290.60049
Wang, Xuejun; Prakasa Rao, B. L. S.; Hu, Shuhe; Yang, Wenzhi
2012
Complete consistency of the estimator of nonparametric regression models based on $$\tilde{\rho}$$-mixing sequences. Zbl 1256.62021
Wang, Xuejun; Xia, Fengxi; Ge, Meimei; Hu, Shuhe; Yang, Wenzhi
2012
Some inequalities for demimartingales and $$N$$-demimartingales. Zbl 1241.60012
Hu, Shuhe; Wang, Xinghui; Yang, Wenzhi; Wang, Xuejun
2012
Convergence rates in the strong law of large numbers for martingale difference sequences. Zbl 1253.60045
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui
2012
The Berry-Esseen bounds for kernel density estimator under dependent sample. Zbl 1283.62080
Yang, Wenzhi; Hu, Shuhe
2012
Complete convergence for moving average process of martingale differences. Zbl 1261.60038
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
2012
Complete convergence and complete moment convergence for a class of random variables. Zbl 1278.60061
Wang, Xinghui; Hu, Shuhe
2012
Complete convergence for arrays of rowwise NOD random variables. Zbl 1289.60047
Shen, Yan; Wang, Xuejun; Hu, Shuhe
2012
Some convergence properties for $$\varphi$$-mixing sequences. Zbl 1289.60048
Shen, Yan; Zhang, Yongjun; Wang, Xuejun; Hu, Shuhe
2012
Strong limit theorems for weighted sums of NOD sequence and exponential inequalities. Zbl 1234.60035
Wang, Xuejun; Hu, Shuhe; Volodin, Andrei I.
2011
An exponential inequality for a NOD sequence and a strong law of large numbers. Zbl 1205.60068
Wang, Xuejun; Hu, Shuhe; Shen, Aiting; Yang, Wenzhi
2011
Strong limit theorems for weighted sums of negatively associated random variables. Zbl 1208.60028
Wang, Xuejun; Li, Xiaoqin; Hu, Shuhe; Yang, Wenzhi
2011
Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables. Zbl 1235.60026
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2011
The Bahadur representation for sample quantiles under strongly mixing sequence. Zbl 1209.62116
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2011
The Bahadur representation for sample quantile under NOD sequence. Zbl 1359.62156
Li, Xiaoqin; Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
2011
The tail probability of the product of dependent random variables from max-domains of attraction. Zbl 1227.60018
Yang, Yingying; Hu, Shuhe; Wu, Tao
2011
Maximal inequalities for some dependent sequences and their applications. Zbl 1296.60041
Hu, Shuhe; Li, Xiaoqin; Yang, Wenzhi; Wang, Xuejun
2011
Maximal inequalities for $$N$$-demimartingale and strong law of large numbers. Zbl 1223.60019
Wang, Xuejun; Hu, Shuhe; Prakasa Rao, B. L. S.; Yang, Wenzhi
2011
Berry-Esséen bound of sample quantiles for negatively associated sequence. Zbl 1395.62106
Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun; Zhang, Qinchi
2011
Some exponential inequalities for acceptable random variables and complete convergence. Zbl 1276.60020
Shen, Aiting; Hu, Shuhe; Volodin, Andrei; Wang, Xuejun
2011
Some new results for demimartingales. Zbl 1240.60086
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Shen, Yan
2011
Strong limit theorems for $$(\alpha,\beta)$$-mixing random variable sequences. Zbl 1265.60058
Shen, Yan; Zhang, Yongjun; Wang, Xuejun; Hu, Shuhe
2011
On complete convergence for arrays of rowwise strong mixing random variables. Zbl 1249.60094
Zhou, Xingcai; Lin, Jinguan; Wang, Xuejun; Hu, Shuhe
2011
Exponential inequalities and inverse moment for NOD sequence. Zbl 1186.60015
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Ling, Nengxiang
2010
On complete convergence for weighted sums of $$\varphi$$-mixing random variables. Zbl 1208.60031
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Shen, Yan
2010
Exponential inequalities and complete convergence for a LNQD sequence. Zbl 1294.60037
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Li, Xiaoqin
2010
Convergence properties for asymptotically almost negatively associated sequence. Zbl 1207.60025
Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi
2010
Doob’s type inequality and strong law of large numbers for demimartingales. Zbl 1197.60021
Wang, Xuejun; Hu, Shuhe; Zhao, Ting; Yang, Wenzhi
2010
Maximal inequality for $$\psi$$-mixing sequences and its applications. Zbl 1197.60031
Wang, Xuejun; Hu, Shuhe; Shen, Yan; Yang, Wenzhi
2010
...and 26 more Documents
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Cited by 405 Authors

 135 Wang, Xuejun 81 Hu, Shuhe 46 Shen, Aiting 46 Wu, Yi 45 Yang, Wenzhi 21 Sung, Soohak 20 Volodin, Andrei I. 20 Wu, Qunying 17 Wang, Xinghui 16 Chen, Pingyan 16 Deng, Xin 14 Li, Xiaoqin 13 Huang, Haiwu 13 Shen, Yan 10 Ding, Liwang 10 Wu, Yongfeng 9 Chen, Ping 9 Xi, Mengmei 9 Yu, Wei 8 Miao, Yu 8 Zhang, Qingxia 7 Hu, Tienchung 7 Liu, Xinsheng 7 Lu, Chao 7 Wu, Ranchao 6 Lu, Dawei 6 Wang, Dingcheng 5 Chen, Ling 5 Chen, Zhiyong 5 Feng, Fengxiang 5 Ge, Meimei 5 Hu, Hongchang 5 Li, Yongming 5 Ling, Nengxiang 5 Wang, Wenjuan 5 Yan, Jigao 5 Yu, Yuncai 4 Ko, Mi-Hwa 4 Ning, Mingming 4 Peng, Jiangyan 4 Rosalsky, Andrew 4 Tang, Xufei 4 Wang, Shijie 4 Wu, Caoqing 4 Xu, Chen 4 Zhang, Shuili 4 Zhang, Ying 4 Zheng, Lulu 3 Amini-Dehak, Mohammad 3 Bozorgnia, Abolghasem 3 Chen, Kan 3 Christofides, Tasos C. 3 Fazekas, István 3 Hu, Xueping 3 Jiang, Yuanying 3 Li, Wei 3 Ling, Jimin 3 Lita da Silva, João 3 Liu, Ling 3 Liu, Tingting 3 Liu, Xiangdong 3 Meng, Bing 3 Prakasa Rao, B. L. S. 3 Qu, Cong 3 Shi, Xiaoping 3 Sun, Yan 3 Tang, Ling 3 Xia, Fengxi 3 Xia, Hao 3 Xu, Huai 3 Yao, Mei 3 Zhang, Yong 3 Zhang, Yu 3 Zhang, Yu 3 Zhao, Ting 3 Zhou, Xingcai 3 Zhu, Huayan 3 Zou, Hang 2 Balakrishnan, Narayanaswamy 2 Chen, Lamei 2 Chen, Yu 2 Chen, Zhuang 2 Cheng, Dongya 2 Cheng, Pan 2 Cheng, Zhaoyang 2 Ding, Shengnan 2 Ding, Yang 2 Durastanti, Claudio 2 Flegal, James M. 2 Fu, Fangning 2 Gao, Miaomiao 2 Gao, Min 2 Hadjikyriakou, Milto 2 Hashorva, Enkelejd 2 He, Qihui 2 Hien, Nguyen Thi Thanh 2 Hou, Tiantian 2 Jones, Galin L. 2 Lang, Junjun 2 Li, Penghua ...and 305 more Authors
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Cited in 84 Serials

 62 Communications in Statistics. Theory and Methods 61 Journal of Inequalities and Applications 26 Statistical Papers 23 Statistics & Probability Letters 21 Journal of Mathematical Inequalities 17 Statistics 17 Discrete Dynamics in Nature and Society 15 Stochastics 13 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 11 Journal of Mathematical Analysis and Applications 11 Abstract and Applied Analysis 8 Filomat 8 Acta Mathematica Sinica. English Series 6 Communications in Statistics. Simulation and Computation 6 Journal of Statistical Computation and Simulation 6 Test 6 Applied Mathematics. Series B (English Edition) 5 Metrika 5 Bulletin of the Korean Mathematical Society 5 Acta Mathematica Hungarica 5 Journal of the Korean Statistical Society 4 Theory of Probability and its Applications 4 Acta Mathematicae Applicatae Sinica. English Series 4 Journal of Nonparametric Statistics 4 Probability in the Engineering and Informational Sciences 4 Open Mathematics 3 Acta Mechanica 3 Kybernetika 3 Insurance Mathematics & Economics 3 Chinese Annals of Mathematics. Series B 3 Methodology and Computing in Applied Probability 2 Lithuanian Mathematical Journal 2 Annals of the Institute of Statistical Mathematics 2 Journal of the Korean Mathematical Society 2 Journal of Statistical Planning and Inference 2 Mathematica Slovaca 2 Probability and Mathematical Statistics 2 Applications of Mathematics 2 Revista Matemática Complutense 2 Journal of Systems Science and Complexity 2 Frontiers of Mathematics in China 2 Journal of Statistical Theory and Practice 2 Modern Stochastics. Theory and Applications 2 AIMS Mathematics 1 The Canadian Journal of Statistics 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Journal of Applied Probability 1 Journal of Computational and Applied Mathematics 1 Monatshefte für Mathematik 1 Systems & Control Letters 1 Journal of Time Series Analysis 1 Stochastic Analysis and Applications 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Science in China. Series A 1 Siberian Advances in Mathematics 1 Computational Statistics 1 International Journal of Computer Mathematics 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Computational Statistics and Data Analysis 1 Theory of Probability and Mathematical Statistics 1 Mathematical Methods of Statistics 1 Journal of Mathematical Sciences (New York) 1 Bernoulli 1 Soft Computing 1 Australian & New Zealand Journal of Statistics 1 Journal of Applied Statistics 1 Brazilian Journal of Probability and Statistics 1 Journal of Applied Mathematics 1 Stochastic Models 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Stochastics and Dynamics 1 Statistical Methods and Applications 1 Thailand Statistician 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 AStA. Advances in Statistical Analysis 1 Electronic Journal of Statistics 1 Science China. Mathematics 1 Journal of Computational and Graphical Statistics 1 Sankhyā. Series A 1 Journal of Applied Mathematics & Informatics 1 Journal of Mathematics 1 East Asian Journal on Applied Mathematics
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Cited in 16 Fields

 341 Probability theory and stochastic processes (60-XX) 233 Statistics (62-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Numerical analysis (65-XX) 3 Mechanics of deformable solids (74-XX) 3 Systems theory; control (93-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)