Berry–Esséen theorem for sample quantiles of asymptotically uncorrelated non reversible Markov chains

ABSTRACT

We prove Berry–Esséen bound for sample quantiles of Markov chains with spectral gap in L².

KEYWORDS:

• ϱ-Mmixing
• Markov chains
• Normal approximation
• Sample quantiles.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F05
• 60J05
• 62E20
• 62F12

Acknowledgments

The author thanks anonymous referee for careful reading and many comments and suggestions that considerably improved this article. Thanks go also to Wojtek Niemiro for references related to quantile regression and estimation of quantiles and spectral (asymptotic) variance.