The Annals of Probability

Asymptotic Expansions for Sample Quantiles

R.-D. Reiss

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

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