A proof of the asymptotic equivalence of two-tail probability approximations

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Abstract

This article considers asymptotic approximations to tail probabilities of a random variable whose distribution depends on a parameter n heuristically representing sample size. Random variables considered have cumulant generating functions with properties similar to that of sums of independent and identically distributed random variables. Probability approximations of Robinson (1982) and Lugannani and Rice (1980) are shown to be equivalent to a relative size O(1/n), under regularity conditions no stronger than the weaker of those necessary to prove either of the two approximations. Applications to permutation testing are discussed.

Original languageEnglish (US)
Pages (from-to)221-228
Number of pages8
JournalCommunications in Statistics - Theory and Methods
Volume36
Issue number2
DOIs
StatePublished - Jan 2007

ASJC Scopus subject areas

  • Statistics and Probability

Keywords

  • Asymptotics
  • Saddlepoint

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