Comparison Inequalities for Order Statistics of Gaussian Arrays

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Abstract

Normal comparison lemma and Slepian’s inequality are essential tools for the analysis of extremes of Gaussian processes. In this paper we show that the Normal comparison lemma for Gaussian vectors can be extended to order statistics of Gaussian arrays. Our applications include the derivation of mixed Gumbel limit laws for the order statistics of stationary Gaussian processes and the investigation of lower tail behavior of order statistics of self-similar Gaussian processes.

Original languageEnglish
Pages (from-to)93-116
Number of pages24
JournalAlea (Rio de Janeiro)
Volume14
Issue number1
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Normal comparison inequality
  • Slepian’s inequality
  • conjunction probability
  • lower tail probability
  • mixed Gumbel limit theorem
  • order statistics process
  • self-similar Gaussian process

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