An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Abstract

Let $(U_n(t){)}_{t\in {\mathbb{R}}^d}$ be the empirical process associated to an ${\mathbb{R}}^d$-valued stationary process $(X_i{)}_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i){)}_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t){)}_{t\in {\mathbb{R}}^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.

to appear in Journal of Theoretical Probability

Cited by in corpus (2)

• A Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains
• Approximating class approach for empirical processes of dependent sequences indexed by functions