Generalizations of maximal inequalities to arbitrary selection rules

Jiantao Jiao; Yanjun Han; Tsachy Weissman

doi:10.1016/j.spl.2018.01.002

Generalizations of maximal inequalities to arbitrary selection rules

Jiantao Jiao, Yanjun Han, Tsachy Weissman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.

Original language	English (US)
Pages (from-to)	19-25
Number of pages	7
Journal	Statistics and Probability Letters
Volume	137
DOIs	https://doi.org/10.1016/j.spl.2018.01.002
State	Published - Jun 2018

Keywords

Convex duality
Entropy
Generalized Holder's inequality
Maximal inequality
Orlicz function

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2018.01.002

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abstract = "We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.",

keywords = "Convex duality, Entropy, Generalized Holder's inequality, Maximal inequality, Orlicz function",

author = "Jiantao Jiao and Yanjun Han and Tsachy Weissman",

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T1 - Generalizations of maximal inequalities to arbitrary selection rules

AU - Jiao, Jiantao

AU - Han, Yanjun

AU - Weissman, Tsachy

PY - 2018/6

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AB - We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.

KW - Convex duality

KW - Entropy

KW - Generalized Holder's inequality

KW - Maximal inequality

KW - Orlicz function

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SP - 19

EP - 25

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Generalizations of maximal inequalities to arbitrary selection rules

Abstract

Keywords

ASJC Scopus subject areas

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