Exponential inequalities for unbounded functions of geometrically ergodic Markov chains: applications to quantitative error bounds for regenerative Metropolis algorithms. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Wintenberger, Olivier
• Is Part Of: Statistics. Volume 51:Issue 1(2017)
• Page Start: 222
• Page End: 234
• Publication Date: 2017-01-02
• Subjects: Markov chains -- exponential inequalities -- Metropolis algorithm -- confidence interval; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2016.1268205
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The aim of this note is to investigate the concentration properties of unbounded functions of geometrically ergodic Markov chains. We derive concentration properties of centred functions with respect to the square of Lyapunov's function in the drift condition satisfied by the Markov chain. We apply the new exponential inequalities to derive confidence intervals for Markov Chain Monte Carlo algorithms. Quantitative error bounds are provided for the regenerative Metropolis algorithm of [Brockwell and Kadane Identification of regeneration times in MCMC simulation, with application to adaptive schemes. J Comput Graphical Stat. 2005;14(2)].