A Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains

TL;DR

This paper establishes a sequential empirical central limit theorem for dependent data from processes with multiple mixing conditions, applicable to Markov chains and dynamical systems, with practical applications to Lipschitz models.

Contribution

It introduces a new CLT for sequential empirical processes under multiple mixing, extending results to Markov chains and dynamical systems with spectral gap properties.

Findings

Proves a CLT for dependent data with multiple mixing.

Applies results to B-geometrically ergodic Markov chains.

Demonstrates usefulness in Lipschitz contraction models.

Abstract

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F. This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron--Frobenius or Markov operator, respectively, has a spectral gap on a restricted space. We provide applications to iterative Lipschitz models that contract on average.