Upper bounds on product and multiplier empirical processes

被引：34

作者：

Mendelson, Shahar ^{[1
]}

机构：

[1] IIT, Technion, Dept Math, IL-32000 Haifa, Israel

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 12期

基金：

以色列科学基金会;

关键词：

Empirical processes; Generic chaining; RANDOM-VARIABLES; CANONICAL PROCESSES; MOMENTS; TAILS; SUMS;

D O I：

10.1016/j.spa.2016.04.019

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study two empirical processes of special structure: firstly, the centred multiplier process indexed by a class F, f -> vertical bar Sigma(N)(i=1) (xi(i) f(X-i) - Epsilon xi f) vertical bar, where the i.i.d. multipliers (xi(i))(i=1)(N) need not be independent of (X-i)(i=1)(N), and secondly, (f, h) -> vertical bar Sigma(N)(i=1) (f(X-i)h(X-i) -Epsilon fh) vertical bar, the centred product process indexed by the classes F and H. We use chaining methods to obtain high probability upper bounds on the suprema of the two processes using a natural variation of Talagrand's gamma-functionals. (C) 2016 Published by Elsevier B.V.

引用

页码：3652 / 3680

页数：29

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