Asymptotic Expansion of Quantiles Computed from Mixed Samples 1

Abstract

This article describes an Edgeworth type expansion as n→∞ for the distribution of a quantile computed from a mixed sample of size nk, representing a finite number k of populations, a sample of size n being drawn from the jth population (l⩽j⩽k). If the sth (s ≧ 3) derivative of each of the underlying k distribution functions exists in the neighbourhood of a suitably defined population quantile, then the error of this asymptotic expansion is of order smaller than n-^(8-2)|2.