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

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 $d$.

10 pages