EFFICIENT SHAPE-CONSTRAINED INFERENCE FOR THE AUTOCOVARIANCE SEQUENCE FROM A REVERSIBLE MARKOV CHAIN

• 成果类型: Article
• 署名作者: Berg, Stephen; Song, Hyebin
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2335
• 发表日期: 2023
• 页码: 2440-2470
• 关键词: spectral variance estimators; width output analysis; monte-carlo; geometric ergodicity; strong consistency; CONVERGENCE; discrete; hastings; density

摘要

In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true auto -covariance sequence with respect to an l(2) distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.