We prove two Large Deviation Principles (LDP) in the zone of moderate deviation probabilities. First we establish the LDP for conditional distributions of moderate deviations of empirical bootstrap measures given an empirical probability measure. Then we establish the LDP for the joint distributions of an empirical measure and a bootstrap empirical measure. Using these LDPs, similar LDPs for differentiable statistical functionals can be established. The LDPs for moderate deviations of an empirical quantile process and an empirical bootstrap copula function are provided as illustrations of these results. Bibliography: 28 titles.

Original languageEnglish
Pages (from-to)90-115
Number of pages26
JournalJournal of Mathematical Sciences (United States)
Volume204
Issue number1
DOIs
StatePublished - 2015

    Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

ID: 71601827