Limit Theorems for quadratic forms of Markov Chains

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.

22 pages, 2 figures

References in corpus (2)

• Batch means and spectral variance estimators in Markov chain Monte Carlo
• Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo