Lugsail lag windows and their application to MCMC
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Lag windows are commonly used in the time series, steady state simulation, and Markov chain Monte Carlo literature to estimate the long range variances of estimators arising from correlated data. We propose a new lugsail lag window specifically designed for improved finite sample performance. We use this lag window for batch means and spectral variance estimators in Markov chain Monte Carlo simulations to obtain strongly consistent estimators that are biased from above in finite samples and asymptotically unbiased. This quality is particularly useful when calculating effective sample size and using sequential stopping rules where they help avoid premature termination. Further, we calculate the bias and variance of lugsail estimators and demonstrate that there is little loss compared to other estimators. We also show mean square consistency of these estimators under weak conditions. Finite sample properties of lugsail estimators are studied in various examples.
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