On the Bahadur Representation of Sample Quantiles for Sequences of phi-Mixing Random Variables

摘要

The object of the present investigation is to show that the elegant asymptotic almost sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur (1966) holds for a stationary sequence of phi-mixing random variables. Two different orders of the remainder term, under different phi-mixing conditions, are obtained and used for proving a functional central limit theorem for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary phi-mixing processes. (Author)