The Annals of Probability

Asymptotic Expansions for Sample Quantiles

R.-D. Reiss

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Abstract

This paper deals with an Edgeworth-type expansion for the distribution of a sample quantile. As the sample size $n$ increases, these expansions establish a higher order approximation which holds uniformly for all Borel sets. If the underlying distribution function has $s + 2$ left and right derivatives at the true quantile, the error of the approximation is of order $O(n^{-(s+1)})$. From this result asymptotic expansions for the distribution functions of sample quantiles and for percentage points are derived.

Article information

Source
Ann. Probab., Volume 4, Number 2 (1976), 249-258.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996132

Digital Object Identifier
doi:10.1214/aop/1176996132

Mathematical Reviews number (MathSciNet)
MR402868

Zentralblatt MATH identifier
0339.60017

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G35: Robustness

Keywords
Sample quantiles Edgeworth expansions percentage points

Citation

Reiss, R.-D. Asymptotic Expansions for Sample Quantiles. Ann. Probab. 4 (1976), no. 2, 249--258. doi:10.1214/aop/1176996132. https://projecteuclid.org/euclid.aop/1176996132


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