Generalizations of Maximal Inequalities to Arbitrary Selection Rules
Probability
2017-08-31 v1
Abstract
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of jointly distributed random variables. We control the expectation of a randomly selected random variable from 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 were introduced in the process, which may be of independent interest.
Cite
@article{arxiv.1708.09041,
title = {Generalizations of Maximal Inequalities to Arbitrary Selection Rules},
author = {Jiantao Jiao and Yanjun Han and Tsachy Weissman},
journal= {arXiv preprint arXiv:1708.09041},
year = {2017}
}