# Multivariate initial sequence estimators in Markov chain Monte Carlo

Ning Dai, Galin Jones

Research output: Contribution to journalArticle

6 Citations (Scopus)

### Abstract

Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a vector of sample means. Geyer (1992) developed a Monte Carlo error estimation method for estimating a univariate mean. We propose a novel multivariate version of Geyer's method that provides an asymptotically valid estimator for the covariance matrix and results in stable Monte Carlo estimates. The finite sample properties of the proposed method are investigated via simulation experiments.

Original language English (US) 184-199 16 Journal of Multivariate Analysis 159 https://doi.org/10.1016/j.jmva.2017.05.009 Published - Jul 1 2017

### Fingerprint

Covariance matrix
Markov Chain Monte Carlo
Markov processes
Estimator
Normal distribution
Error analysis
Multivariate Normal Distribution
Sample mean
Error Estimation
Simulation Methods
Simulation Experiment
Univariate
Valid
Experiments
Estimate
Markov chain Monte Carlo

### Keywords

• Central limit theorem
• Covariance matrix estimation
• Gibbs sampler
• Markov chain Monte Carlo
• Metropolis–Hastings algorithm

### Cite this

In: Journal of Multivariate Analysis, Vol. 159, 01.07.2017, p. 184-199.

Research output: Contribution to journalArticle

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KW - Covariance matrix estimation

KW - Gibbs sampler

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KW - Metropolis–Hastings algorithm

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