The Bahadur representation of sample quantiles for associated sequences

TL;DR

This paper derives the Bahadur representation for sample quantiles in associated sequences, showing how the approximation rate depends on covariance decay and approaches the independent case when covariances diminish rapidly.

Contribution

It extends Bahadur representation results to associated sequences with polynomial covariance decay, highlighting the influence of covariance decay on approximation rates.

Findings

Approximate rate depends on covariance decay degree.

Rate approaches optimal under independence with fast covariance decay.

Provides theoretical foundation for quantile analysis in dependent sequences.

Abstract

In this paper, the Bahadur representation of sample quantiles based on associated sequences is established under polynomially decaying of covariances. The rate of approximation depends on the covariances decay degree and becomes close to the optimal rate obtained under independence when the covariances decrease fastly to 0.