Fetching the paper…
Reading the bibliography…
Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression.
V. N. Sudakov, Gauss and Cauchy measures and ε \varepsilon -entropy , Dokl. Akad. Nauk SSSR 185
1969
Earlier work this paper cites.
Lucien Le Cam, Convergence of estimates under dimensionality restrictions , Ann. Statist. 1
1973
Earlier work this paper cites.
Jon A. Wellner, Limit theorems for the ratio of the empirical distribution function to the true distribution function , Z. Wahrsch. Verw. Gebiete 45
1978
Earlier work this paper cites.
Ulf Grenander, Abstract Inference , John Wiley & Sons, Inc., New York, 1981, Wiley Series in Probability and Mathematical Statistics
1981
Earlier work this paper cites.
R. M. Dudley, Empirical and Poisson processes on classes of sets or functions too large for central limit theorems , Z. Wahrsch. Verw. Gebiete 61
1982
Earlier work this paper cites.
Winfried Stute, The oscillation behavior of empirical processes , Ann. Probab. 10
1982
Earlier work this paper cites.
Galen R. Shorack and Jon A. Wellner, Limit theorems and inequalities for the uniform empirical process indexed by intervals , Ann. Probab. 10
1982
Earlier work this paper cites.
Lucien Birgé, Approximation dans les espaces métriques et théorie de l’estimation , Z. Wahrsch. Verw. Gebiete 65
1983
Earlier work this paper cites.
David M. Mason, Galen R. Shorack, and Jon A. Wellner, Strong limit theorems for oscillation moduli of the uniform empirical process , Z. Wahrsch. Verw. Gebiete 65
1983
Earlier work this paper cites.
by same author, The oscillation behavior of empirical processes: the multivariate case , Ann. Probab. 12
1984
Earlier work this paper cites.
Kenneth S. Alexander, Rates of growth and sample moduli for weighted empirical processes indexed by sets , Probab. Theory Related Fields 75
1987
Earlier work this paper cites.
Mina Ossiander, A central limit theorem under metric entropy with L 2 L_{2} bracketing , Ann. Probab. 15
1987
Earlier work this paper cites.
Sara van de Geer, A new approach to least-squares estimation, with applications , Ann. Statist. 15
1987
Earlier work this paper cites.
Tim Robertson, F. T. Wright, and R. L. Dykstra, Order restricted statistical inference , Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1988
1988
Earlier work this paper cites.
by same author, Estimating a regression function , Ann. Statist. 18
1990
Earlier work this paper cites.
A. P. Korostelëv and A. B. Tsybakov, Asymptotically minimax image reconstruction problems , Topics in nonparametric estimation, Adv. Soviet Math., vol. 12, Amer. Math. Soc., Providence, RI, 1992, pp. 45–86
1992
Earlier work this paper cites.
Lucien Birgé and Pascal Massart, Rates of convergence for minimum contrast estimators , Probab. Theory Related Fields 97
1993
Earlier work this paper cites.
by same author, Minimax theory of image reconstruction , Lecture Notes in Statistics, vol. 82, Springer-Verlag, New York, 1993
1993
Earlier work this paper cites.
by same author, Hellinger-consistency of certain nonparametric maximum likelihood estimators , Ann. Statist. 21
1993
Earlier work this paper cites.
Enno Mammen and Alexandre B. Tsybakov, Asymptotical minimax recovery of sets with smooth boundaries , Ann. Statist. 23
1995
Earlier work this paper cites.
by same author, The method of sieves and minimum contrast estimators , Math. Methods Statist. 4
1995
Cited alongside, same era.
Wing Hung Wong and Xiaotong Shen, Probability inequalities for likelihood ratios and convergence rates of sieve MLEs , Ann. Statist. 23
1995
Cited alongside, same era.
Luc Devroye, László Györfi, and Gábor Lugosi, A Probabilistic Theory of Pattern Recognition , Applications of Mathematics (New York), vol. 31, Springer-Verlag, New York, 1996
1996
Cited alongside, same era.
Michel Talagrand, New concentration inequalities in product spaces , Invent. Math. 126
1996
Cited alongside, same era.
Aad van der Vaart, Efficient maximum likelihood estimation in semiparametric mixture models , Ann. Statist. 24
1996
Cited alongside, same era.
Guillaume Lecué, Simultaneous adaptation to the margin and to complexity in classification , Ann. Statist. 35
2007
Later among the works it cites.
Arseni Seregin and Jon A. Wellner, Nonparametric estimation of multivariate convex-transformed densities , Ann. Statist. 38
2010
Later among the works it cites.
Adityanand Guntuboyina, Optimal rates of convergence for convex set estimation from support functions , Ann. Statist. 40
2012
Later among the works it cites.
Adrien Saumard, Optimal upper and lower bounds for the true and empirical excess risks in heteroscedastic least-squares regression , Electron. J. Stat. 6
2012
Later among the works it cites.
Victor-Emmanuel Brunel, Adaptive estimation of convex polytopes and convex sets from noisy data , Electron. J. Stat. 7
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
by same author, New Donsker classes , Ann. Probab. 24
1996
Cited alongside, same era.
Aad van der Vaart and Jon A. Wellner, Weak Convergence and Empirical Processes , Springer Series in Statistics, Springer-Verlag, New York, 1996
1996
Cited alongside, same era.
Andrew Barron, Lucien Birgé, and Pascal Massart, Risk bounds for model selection via penalization , Probab. Theory Related Fields 113
1999
Cited alongside, same era.
by same author, Smooth discrimination analysis , Ann. Statist. 27
1999
Cited alongside, same era.
1999
Cited alongside, same era.
Evarist Giné, Rafał Latała, and Joel Zinn, Exponential and moment inequalities for U U -statistics , High dimensional probability, II (Seattle, WA, 1999), Progr. Probab., vol. 47, Birkhäuser Boston, Boston, MA, 2000, pp. 13–38
2000
Cited alongside, same era.
by same author, Applications of Empirical Process Theory , Cambridge Series in Statistical and Probabilistic Mathematics, vol. 6, Cambridge University Press, Cambridge, 2000
2000
Cited alongside, same era.
Sourav Chatterjee, A new perspective on least squares under convex constraint , Ann. Statist. 42
2014
Later among the works it cites.
by same author, Uniform central limit theorems , second ed., Cambridge Studies in Advanced Mathematics, vol. 142, Cambridge University Press, New York, 2014
2014
Later among the works it cites.
Yannick Baraud, Bounding the expectation of the supremum of an empirical process over a (weak) VC-major class , Electron. J. Stat. 10
2016
Later among the works it cites.
Charles R. Doss and Jon A. Wellner, Global rates of convergence of the MLEs of log-concave and s s -concave densities , Ann. Statist. 44
2016
Later among the works it cites.
Evarist Giné and Richard Nickl, Mathematical foundations of infinite-dimensional statistical models , Cambridge Series in Statistical and Probabilistic Mathematics, [40], Cambridge University Press, New York, 2016
2016
Later among the works it cites.
Qiyang Han and Jon A. Wellner, Approximation and estimation of s s -concave densities via Rényi divergences , Ann. Statist. 44
2016
Later among the works it cites.
Arlene K. H. Kim and Richard J. Samworth, Global rates of convergence in log-concave density estimation , Ann. Statist. 44
2016
Later among the works it cites.
Sara van de Geer and Martin J. Wainwright, On concentration for (regularized) empirical risk minimization , Sankhya A 79
2017
Later among the works it cites.
Timothy Carpenter, Ilias Diakonikolas, Anastasios Sidiropoulos, and Alistair Stewart, Near-optimal sample complexity bounds for maximum likelihood estimation of multivariate log-concave densities , Conference on Learning Theory, 2018, pp. 1–29
2018
Later among the works it cites.
Sabyasachi Chatterjee, Adityanand Guntuboyina, and Bodhisattva Sen, On matrix estimation under monotonicity constraints , Bernoulli 24
2018
Later among the works it cites.
2019
Closest in time.
by same author, Convergence rates of least squares regression estimators with heavy-tailed errors , Ann. Statist. 47
2019
Closest in time.
Qiyang Han, Tengyao Wang, Sabyasachi Chatterjee, and Richard J. Samworth, Isotonic regression in general dimensions , Ann. Statist. 47
2019
Closest in time.