On kernel estimators of density for reversible Markov chains

TL;DR

This paper studies kernel density estimators for stationary reversible Markov chains, introducing a new central limit theorem for such chains under covariance conditions, advancing theoretical understanding.

Contribution

It presents a novel central limit theorem for reversible Markov chains, facilitating analysis of kernel density estimators in this context.

Findings

New CLT for reversible Markov chains

Theoretical foundation for kernel density estimation in Markov processes

Potential applications in statistical inference for dependent data

Abstract

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.