Limit Theorems for quadratic forms of Markov Chains

Yves F. Atchade; Matias D. Cattaneo

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arXiv · 1108.2743

Limit Theorems for quadratic forms of Markov Chains

Yves F. Atchade·Matias D. Cattaneo

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Abstract

We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results to Markov Chain Monte Carlo simulation. As another illustration, we use the method to derive a central limit theorem for U-statistics with varying kernels.

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Yves F. Atchade, Matias D. Cattaneo. 2011-08-13. Limit Theorems for quadratic forms of Markov Chains. https://arxiv.org/abs/1108.2743

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