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April, 1976 Asymptotic Expansions for Sample Quantiles
R.-D. Reiss
Ann. Probab. 4(2): 249-258 (April, 1976). DOI: 10.1214/aop/1176996132

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.

Citation

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R.-D. Reiss. "Asymptotic Expansions for Sample Quantiles." Ann. Probab. 4 (2) 249 - 258, April, 1976. https://doi.org/10.1214/aop/1176996132

Information

Published: April, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0339.60017
MathSciNet: MR402868
Digital Object Identifier: 10.1214/aop/1176996132

Subjects:
Primary: 60F05
Secondary: 62G35

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 2 • April, 1976
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