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

John E. Kolassa

doi:https://doi.org/10.1080/03610920600974187

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

John E. Kolassa

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	221-228
Number of pages	8
Journal	Communications in Statistics - Theory and Methods
Volume	36
Issue number	2
DOIs	https://doi.org/10.1080/03610920600974187
State	Published - Jan 2007

ASJC Scopus subject areas

Statistics and Probability

Keywords

Asymptotics
Saddlepoint

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https://doi.org/10.1080/03610920600974187

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AB - 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.

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KW - Saddlepoint

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

Abstract

ASJC Scopus subject areas

Keywords

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