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August 2018 Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo
Dootika Vats, James M. Flegal, Galin L. Jones
Bernoulli 24(3): 1860-1909 (August 2018). DOI: 10.3150/16-BEJ914

Abstract

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.

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Dootika Vats. James M. Flegal. Galin L. Jones. "Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo." Bernoulli 24 (3) 1860 - 1909, August 2018. https://doi.org/10.3150/16-BEJ914

Information

Received: 1 January 2016; Revised: 1 June 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839254
MathSciNet: MR3757517
Digital Object Identifier: 10.3150/16-BEJ914

Keywords: Markov chain , Monte Carlo , spectral methods , standard errors

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 3 • August 2018
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