Optimal mean squared error bandwidth for spectral variance estimators in MCMC simulations
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This paper proposes optimal mean squared error bandwidths for a family of multivariate spectral variance estimators. The asymptotic mean squared error of the spectral variance estimator is derived under conditions that are convenient to verify for Markov chain Monte Carlo simulations. Optimal bandwidths are obtained by minimizing the asymptotic mean squared error along with techniques to estimate the proportional constant. Auto-regressive examples illustrate the quality of the estimation procedure. Finally, we show optimal bandwidths proposed here outperform current bandwidth selection methods.
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