Generalizations of maximal inequalities to arbitrary selection rules

Jiantao Jiao, Yanjun Han, Tsachy Weissman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)19-25
Number of pages7
JournalStatistics and Probability Letters
StatePublished - Jun 2018


  • 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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