# zbMATH — the first resource for mathematics

## Barron, Andrew Roger

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 Author ID: barron.andrew-r Published as: Barron, A.; Barron, Andrew; Barron, Andrew R. Homepage: http://www.stat.yale.edu/~arb4/ External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 36 Publications since 1985
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#### Co-Authors

 7 single-authored 2 Clarke, Bertrand S. 2 Cover, Thomas Merrill 2 Joseph, Antony 2 Madiman, Mokshay M. 2 Xie, Qun 2 Yang, Yuhong 1 Benšić, Mirta 1 Birgé, Lucien 1 Cheang, Gerald H. L. 1 Cohen, Albert 1 Cross, Jason E. 1 Dahmen, Wolfgang A. 1 DeVore, Ronald A. 1 Györfi, László 1 Hengartner, Nicolas W. 1 Johnson, Oliver Thomas 1 Kagan, Abram Meerovich 1 Kawabata, Tsutomu 1 Klusowski, Jason M. 1 Leung, Gilbert 1 Liang, Feng 1 Massart, Pascal 1 Rissanen, Jorma J. 1 Sabo, Kristian 1 Schervish, Mark J. 1 Sheu, Chyong-Hwa 1 Takeuchi, Jun’ichi 1 Tatikonda, Sekhar 1 Tinghui, Yu. 1 van der Meulen, Edward C. 1 Venkataramanan, Ramji 1 Wasserman, Larry Alan 1 Yang, Xiao 1 Yu, Bin
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#### Serials

 17 IEEE Transactions on Information Theory 6 The Annals of Statistics 2 The Annals of Probability 2 Probability Theory and Related Fields 1 Journal of Approximation Theory 1 Journal of Statistical Planning and Inference 1 Machine Learning 1 Test 1 Journal of Mathematical Sciences (New York) 1 Mathematical Finance 1 Foundations and Trends in Communications and Information Theory
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#### Fields

 23 Statistics (62-XX) 19 Information and communication theory, circuits (94-XX) 5 Approximations and expansions (41-XX) 3 Probability theory and stochastic processes (60-XX) 3 Computer science (68-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

33 Publications have been cited 1,465 times in 1,178 Documents Cited by Year
Universal approximation bounds for superpositions of a sigmoidal function. Zbl 0818.68126
Barron, Andrew R.
1993
Risk bounds for model selection via penalization. Zbl 0946.62036
Barron, Andrew; Birgé, Lucien; Massart, Pascal
1999
The consistency of posterior distributions in nonparametric problems. Zbl 0980.62039
Barron, Andrew; Schervish, Mark J.; Wasserman, Larry
1999
Information-theoretic determination of minimax rates of convergence. Zbl 0978.62008
Yang, Yuhong; Barron, Andrew
1999
Information-theoretic asymptotics of Bayes methods. Zbl 0709.62008
Clarke, Bertrand S.; Barron, Andrew R.
1990
Information theory and mixing least-squares regressions. Zbl 1309.94051
Leung, Gilbert; Barron, Andrew R.
2006
Entropy and the central limit theorem. Zbl 0599.60024
Barron, Andrew R.
1986
Minimum complexity density estimation. Zbl 0743.62003
Barron, Andrew R.; Cover, Thomas M.
1991
Jeffreys’ prior is asymptotically least favorable under entropy risk. Zbl 0820.62006
Clarke, Bertrand S.; Barron, Andrew R.
1994
Approximation of density functions by sequences of exponential families. Zbl 0739.62027
Barron, Andrew R.; Sheu, Chyong-Hwa
1991
The minimum description length principle in coding and modeling. Zbl 0933.94013
Barron, Andrew; Rissanen, Jorma; Yu, Bin
1998
The strong ergodic theorem for densities: Generalized Shannon-McMillan- Breiman theorem. Zbl 0608.94001
Barron, Andrew R.
1985
Approximation and learning by greedy algorithms. Zbl 1138.62019
Barron, Andrew R.; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald A.
2008
Approximation and estimation bounds for artificial neural networks. Zbl 0818.68127
Barron, Andrew R.
1994
Fisher information inequalities and the central limit theorem. Zbl 1047.62005
Johnson, Oliver; Barron, Andrew
2004
Complexity regularization with application to artificial neural networks. Zbl 0739.62001
Barron, Andrew R.
1991
Distribution estimation consistent in total variation and in two types of information divergence. Zbl 0765.62007
Barron, Andrew R.; Györfi, László; van der Meulen, Edward C.
1992
An asymptotic property of model selection criteria. Zbl 0949.62041
Yang, Yuhong; Barron, Andrew R.
1998
Generalized entropy power inequalities and monotonicity properties of information. Zbl 1326.94034
Madiman, Mokshay M.; Barron, Andrew R.
2007
Exact minimax strategies for predictive density estimation, data compression, and model selection. Zbl 1315.94022
Liang, Feng; Barron, Andrew R.
2004
Uniformly powerful goodness of fit tests. Zbl 0674.62032
Barron, Andrew R.
1989
Asymptotic minimax regret for data compression, gambling, and prediction. Zbl 0996.94025
Xie, Qun; Barron, Andrew R.
2000
A better approximation for balls. Zbl 0991.41012
Cheang, Gerald H. L.; Barron, Andrew R.
2000
Information-theoretic characterization of Bayes performance and the choice of priors in parametric and nonparametric problems. (With discussion). Zbl 0974.62020
Barron, Andrew R.
1999
A bound on the financial value of information. Zbl 0662.90023
Barron, Andrew R.; Cover, Thomas M.
1988
Efficient universal portfolios for past-dependent target classes. Zbl 1050.91041
Cross, Jason E.; Barron, Andrew R.
2003
Minimax redundancy for the class of memoryless sources. Zbl 0872.94017
Xie, Qun; Barron, Andrew R.
1997
Contribution to the theory of Pitman estimators. Zbl 1305.62099
Kagan, A. M.; Tinghui, Yu.; Barron, A.; Madiman, M.
2014
Approximation by combinations of ReLU and squared ReLU ridge functions with $$\ell^1$$ and $$\ell^0$$ controls. Zbl 1432.41003
Klusowski, Jason M.; Barron, Andrew R.
2018
Least squares superposition codes of moderate dictionary size are reliable at rates up to capacity. Zbl 1365.94019
Joseph, Antony; Barron, Andrew R.
2012
Information theory and superefficiency. Zbl 0932.62005
Barron, Andrew; Hengartner, Nicolas
1998
Sparse regression codes. Zbl 1429.94047
Venkataramanan, Ramji; Tatikonda, Sekhar; Barron, Andrew
2019
Fast sparse superposition codes have near exponential error probability for $$R<\mathcal C$$. Zbl 1364.94402
Joseph, Antony; Barron, Andrew R.
2014
Sparse regression codes. Zbl 1429.94047
Venkataramanan, Ramji; Tatikonda, Sekhar; Barron, Andrew
2019
Approximation by combinations of ReLU and squared ReLU ridge functions with $$\ell^1$$ and $$\ell^0$$ controls. Zbl 1432.41003
Klusowski, Jason M.; Barron, Andrew R.
2018
Contribution to the theory of Pitman estimators. Zbl 1305.62099
Kagan, A. M.; Tinghui, Yu.; Barron, A.; Madiman, M.
2014
Fast sparse superposition codes have near exponential error probability for $$R<\mathcal C$$. Zbl 1364.94402
Joseph, Antony; Barron, Andrew R.
2014
Least squares superposition codes of moderate dictionary size are reliable at rates up to capacity. Zbl 1365.94019
Joseph, Antony; Barron, Andrew R.
2012
Approximation and learning by greedy algorithms. Zbl 1138.62019
Barron, Andrew R.; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald A.
2008
Generalized entropy power inequalities and monotonicity properties of information. Zbl 1326.94034
Madiman, Mokshay M.; Barron, Andrew R.
2007
Information theory and mixing least-squares regressions. Zbl 1309.94051
Leung, Gilbert; Barron, Andrew R.
2006
Fisher information inequalities and the central limit theorem. Zbl 1047.62005
Johnson, Oliver; Barron, Andrew
2004
Exact minimax strategies for predictive density estimation, data compression, and model selection. Zbl 1315.94022
Liang, Feng; Barron, Andrew R.
2004
Efficient universal portfolios for past-dependent target classes. Zbl 1050.91041
Cross, Jason E.; Barron, Andrew R.
2003
Asymptotic minimax regret for data compression, gambling, and prediction. Zbl 0996.94025
Xie, Qun; Barron, Andrew R.
2000
A better approximation for balls. Zbl 0991.41012
Cheang, Gerald H. L.; Barron, Andrew R.
2000
Risk bounds for model selection via penalization. Zbl 0946.62036
Barron, Andrew; Birgé, Lucien; Massart, Pascal
1999
The consistency of posterior distributions in nonparametric problems. Zbl 0980.62039
Barron, Andrew; Schervish, Mark J.; Wasserman, Larry
1999
Information-theoretic determination of minimax rates of convergence. Zbl 0978.62008
Yang, Yuhong; Barron, Andrew
1999
Information-theoretic characterization of Bayes performance and the choice of priors in parametric and nonparametric problems. (With discussion). Zbl 0974.62020
Barron, Andrew R.
1999
The minimum description length principle in coding and modeling. Zbl 0933.94013
Barron, Andrew; Rissanen, Jorma; Yu, Bin
1998
An asymptotic property of model selection criteria. Zbl 0949.62041
Yang, Yuhong; Barron, Andrew R.
1998
Information theory and superefficiency. Zbl 0932.62005
Barron, Andrew; Hengartner, Nicolas
1998
Minimax redundancy for the class of memoryless sources. Zbl 0872.94017
Xie, Qun; Barron, Andrew R.
1997
Jeffreys’ prior is asymptotically least favorable under entropy risk. Zbl 0820.62006
Clarke, Bertrand S.; Barron, Andrew R.
1994
Approximation and estimation bounds for artificial neural networks. Zbl 0818.68127
Barron, Andrew R.
1994
Universal approximation bounds for superpositions of a sigmoidal function. Zbl 0818.68126
Barron, Andrew R.
1993
Distribution estimation consistent in total variation and in two types of information divergence. Zbl 0765.62007
Barron, Andrew R.; Györfi, László; van der Meulen, Edward C.
1992
Minimum complexity density estimation. Zbl 0743.62003
Barron, Andrew R.; Cover, Thomas M.
1991
Approximation of density functions by sequences of exponential families. Zbl 0739.62027
Barron, Andrew R.; Sheu, Chyong-Hwa
1991
Complexity regularization with application to artificial neural networks. Zbl 0739.62001
Barron, Andrew R.
1991
Information-theoretic asymptotics of Bayes methods. Zbl 0709.62008
Clarke, Bertrand S.; Barron, Andrew R.
1990
Uniformly powerful goodness of fit tests. Zbl 0674.62032
Barron, Andrew R.
1989
A bound on the financial value of information. Zbl 0662.90023
Barron, Andrew R.; Cover, Thomas M.
1988
Entropy and the central limit theorem. Zbl 0599.60024
Barron, Andrew R.
1986
The strong ergodic theorem for densities: Generalized Shannon-McMillan- Breiman theorem. Zbl 0608.94001
Barron, Andrew R.
1985
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#### Cited by 1,491 Authors

 23 Comte, Fabienne 20 Sanguineti, Marcello 16 Costarelli, Danilo 16 Walker, Stephen Grahm 15 Tsybakov, Alexandre B. 14 Kůrková, Věra 13 Gnecco, Giorgio 13 Yang, Yuhong 11 Baraud, Yannick 11 Kohler, Michael 11 Pergamenshchikov, Sergeĭ Markovich 11 Yang, Weiguo 10 Bobkov, Sergey Germanovich 10 Cao, Feilong 10 Temlyakov, Vladimir Nikolaevich 10 Wasserman, Larry Alan 9 Birgé, Lucien 9 Zhang, Xinyu 8 Brunel, Élodie 8 Chistyakov, Gennadiy P. 8 Genon-Catalot, Valentine 8 Götze, Friedrich W. 8 Györfi, László 8 Lacour, Claire 8 Lepskiĭ, Oleg Vital’evich 8 Madiman, Mokshay M. 8 Massart, Pascal 8 Vinti, Gianluca 8 Zhou, Harrison H. 7 Barron, Andrew Roger 7 Clarke, Bertrand S. 7 Gao, Chao 7 Ghosal, Subhashis 7 Ghosh, Jayanta Kumar 7 Ghosh, Malay 7 Grünwald, Peter D. 7 Kainen, Paul C. 7 Lian, Heng 7 Rozenholc, Yves 7 Strawderman, William Edward 7 Van der Vaart, Adrianus Willem 7 Zou, Guohua 6 Alquier, Pierre 6 Dalalyan, Arnak S. 6 Johannes, Jan 6 Komaki, Fumiyasu 6 Lin, Shaobo 6 Mhaskar, Hrushikesh N. 6 Rousseau, Judith 6 Scricciolo, Catia 6 Spigler, Renato 6 Toscani, Giuseppe 6 Vajda, Igor 6 Xu, Xinyi 6 Xu, Zongben 6 Zhang, Tong 5 Alessandri, Angelo 5 Berlinet, Alain F. 5 Cai, Tony Tony 5 Cervellera, Cristiano 5 Choi, Taeryon 5 Dunson, David Brian 5 Giraud, Christophe 5 Johnson, Oliver Thomas 5 Juditsky, Anatoli B. 5 Liang, Hua 5 Maiorov, Vitaly Evgen’evich 5 Marchand, Eric 5 Pati, Debdeep 5 Rigollet, Philippe 5 Van de Geer, Sara Anna 4 Anastassiou, George Angelos 4 Arlot, Sylvain 4 Berger, James Orvis 4 Biau, Gérard 4 Bunea, Florentina 4 Candès, Emmanuel J. 4 Carlen, Eric Anders 4 Castillo, Ismaël 4 E, Weinan 4 Fourdrinier, Dominique 4 George, Edward I. 4 Golubev, Yuriĭ K. 4 Grigor’ev, Dmitriĭ Yur’evich 4 Guilloux, Agathe 4 Hahm, Nahmwoo 4 Huet, Sylvie 4 Hutter, Marcus 4 Jordan, Michael Irwin 4 Judd, Kevin 4 Kagan, Abram Meerovich 4 Kim, Yongdai 4 Koo, Ja-Yong 4 La Rocca, Michele 4 Lecué, Guillaume 4 Martin, Ryan R. 4 Mees, Alistair I. 4 Nourdin, Ivan 4 Peccati, Giovanni 4 Perna, Cira ...and 1,391 more Authors
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#### Cited in 258 Serials

 135 The Annals of Statistics 54 Electronic Journal of Statistics 52 Journal of Statistical Planning and Inference 36 Bernoulli 29 Neural Networks 29 Neural Computation 27 Journal of Multivariate Analysis 23 Journal of Econometrics 23 Stochastic Processes and their Applications 21 Statistics & Probability Letters 20 Journal of Nonparametric Statistics 18 Annals of the Institute of Statistical Mathematics 18 Automatica 18 Probability Theory and Related Fields 17 Communications in Statistics. Theory and Methods 17 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 15 Journal of Approximation Theory 14 Statistical Science 14 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 13 Computational Statistics and Data Analysis 12 Scandinavian Journal of Statistics 12 Test 11 Journal of Complexity 11 Econometric Theory 10 Journal of Statistical Physics 10 European Journal of Operational Research 9 Journal of the American Statistical Association 9 Mathematical Methods of Statistics 8 Applied Mathematics and Computation 8 Journal of Mathematical Psychology 8 Theoretical Computer Science 8 Sankhyā. Series A 7 Journal of Functional Analysis 7 Statistics 7 Pattern Recognition 7 Applied and Computational Harmonic Analysis 7 Journal of the Royal Statistical Society. Series B. Statistical Methodology 6 Journal of Mathematical Analysis and Applications 6 Journal of Mathematical Physics 6 Metrika 6 The Annals of Probability 6 Journal of Computer and System Sciences 6 Journal of Optimization Theory and Applications 6 Constructive Approximation 6 Entropy 6 Science China. Mathematics 6 Bayesian Analysis 5 Journal of Computational Physics 5 Kybernetika 5 Physica D 5 Journal of Theoretical Probability 5 Machine Learning 5 Journal of Mathematical Sciences (New York) 5 Advances in Computational Mathematics 5 Mathematical Finance 5 Journal of Machine Learning Research (JMLR) 5 Analysis and Applications (Singapore) 4 Computers & Mathematics with Applications 4 Communications in Mathematical Physics 4 Problems of Information Transmission 4 International Statistical Review 4 Ricerche di Matematica 4 Information and Computation 4 Mathematical and Computer Modelling 4 Foundations of Computational Mathematics 4 Proceedings of the Steklov Institute of Mathematics 3 The Canadian Journal of Statistics 3 Mathematical Notes 3 Fuzzy Sets and Systems 3 Information Sciences 3 Results in Mathematics 3 Computers & Operations Research 3 International Journal of Approximate Reasoning 3 Applied Mathematics Letters 3 Journal of Statistical Computation and Simulation 3 Proceedings of the National Academy of Sciences of the United States of America 3 Computational Optimization and Applications 3 Statistical Papers 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Statistical Inference for Stochastic Processes 3 Probability in the Engineering and Informational Sciences 3 Journal of Applied Mathematics 3 International Journal of Wavelets, Multiresolution and Information Processing 3 Statistical Methods and Applications 3 Statistical Methodology 3 The Annals of Applied Statistics 3 Statistics and Computing 2 Biological Cybernetics 2 Discrete Applied Mathematics 2 Information Processing Letters 2 Mathematical Methods in the Applied Sciences 2 Advances in Mathematics 2 Journal of Computational and Applied Mathematics 2 Journal of Mathematical Economics 2 Mathematische Nachrichten 2 Numerical Functional Analysis and Optimization 2 Operations Research 2 Systems & Control Letters 2 Insurance Mathematics & Economics 2 Journal of Time Series Analysis ...and 158 more Serials
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#### Cited in 41 Fields

 720 Statistics (62-XX) 211 Probability theory and stochastic processes (60-XX) 181 Computer science (68-XX) 149 Numerical analysis (65-XX) 114 Information and communication theory, circuits (94-XX) 102 Approximations and expansions (41-XX) 80 Biology and other natural sciences (92-XX) 53 Operations research, mathematical programming (90-XX) 52 Systems theory; control (93-XX) 51 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 30 Functional analysis (46-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 19 Partial differential equations (35-XX) 19 Statistical mechanics, structure of matter (82-XX) 16 Real functions (26-XX) 16 Dynamical systems and ergodic theory (37-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 16 Convex and discrete geometry (52-XX) 14 Operator theory (47-XX) 14 Quantum theory (81-XX) 7 Fluid mechanics (76-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Combinatorics (05-XX) 5 Measure and integration (28-XX) 5 Integral transforms, operational calculus (44-XX) 5 Differential geometry (53-XX) 4 Special functions (33-XX) 4 Ordinary differential equations (34-XX) 3 General and overarching topics; collections (00-XX) 3 Mathematical logic and foundations (03-XX) 3 Number theory (11-XX) 3 Functions of a complex variable (30-XX) 3 Integral equations (45-XX) 2 History and biography (01-XX) 2 Mechanics of deformable solids (74-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX)