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We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics.
Wassily Hoeffding, A combinatorial central limit theorem , Ann. Math. Statistics 22
1951
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by same author, Probability inequalities for sums of bounded random variables , J. Amer. Statist. Assoc. 58
1963
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E. Bolthausen, An estimate of the remainder in a combinatorial central limit theorem , Z. Wahrsch. Verw. Gebiete 66
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Michel Ledoux and Michel Talagrand, Probability in Banach spaces , Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 23, Springer-Verlag, Berlin, 1991, Isoperimetry and processes. MR 1102015
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Michel Ledoux, On Talagrand’s deviation inequalities for product measures , ESAIM Probab. Statist. 1
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Michel Talagrand, New concentration inequalities in product spaces , Invent. Math. 126
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Fuqing Gao and Jeremy Quastel, Exponential decay of entropy in the random transposition and Bernoulli-Laplace models , Ann. Appl. Probab. 13
2003
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Sergey G. Bobkov and Prasad Tetali, Modified logarithmic Sobolev inequalities in discrete settings , J. Theoret. Probab. 19
2006
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Sourav Chatterjee, Stein’s method for concentration inequalities , Probab. Theory Related Fields 138
2007
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Willliam Feller, An introduction to probability theory and its applications, vol 2 , John Wiley & Sons, 2008
2008
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David Gross and Vincent Nesme, Note on sampling without replacing from a finite collection of matrices , 2010
2010
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Stéphane Boucheron, Gábor Lugosi, and Pascal Massart, Concentration inequalities. A nonasymptotic theory of independence , Oxford University Press, Oxford, 2013. MR 3185193
2013
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Kyle Luh and Nicholas Pippenger, Large-deviation bounds for sampling without replacement , Amer. Math. Monthly 121
2014
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2014
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Bernard Bercu, Bernard Delyon, and Emmanuel Rio, Concentration inequalities for sums and martingales , SpringerBriefs in Mathematics, Springer, Cham, 2015. MR 3363542
2015
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2019
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