A note on weak convergence of the sequential multivariate empirical process under strong mixing

TL;DR

This paper studies the weak convergence of the sequential multivariate empirical process under strong mixing conditions, providing improved convergence results for certain mixing rates that depend on the sample size.

Contribution

It offers new weak convergence results for the multivariate empirical process under strong mixing with specific mixing rate conditions, improving previous dimension-dependent results.

Findings

Weak convergence established for mixing rates _n = O(n^{-a}) with a > 1

Improved convergence results compared to existing literature

Results depend on mixing rates and dimension d

Abstract

This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing results in the literature that are based on mixing rates depending on the dimension $d$.