Transcription of On the Markov Chain Central Limit Theorem - Statistics
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On the Markov Chain Central Limit Theorem - Statistics
On the Markov Chain Central Limit TheoremGalin L. JonesSchool of StatisticsUniversity of MinnesotaMinneapolis, MN, goal of this paper is to describe conditions which guarantee a Central Limit Theorem forfunctionals of general state space Markov chains. This is done with a view towards Markovchain Monte Carlo settings and hence the focus is on the connections between drift and mixingconditions and their implications. In particular, we consider three commonly cited Central limittheorems and discuss their relationship to classical results for mixing processes. Several motivat-ing examples are given which range from toy one-dimensionalsettings to complicated settingsencountered in Markov Chain Monte IntroductionLetX={Xi:i= 0,1,2,..}be a Harris ergodic Markov Chain on a general spaceXwithinvariant probability distribution having supportX. Letfbe a Borel function and define fn:=n 1 ni=1f(Xi) and E f:= Xf(x) (dx).
On the Markov Chain Central Limit Theorem Galin L. Jones School of Statistics University of Minnesota Minneapolis, MN, USA galin@stat.umn.edu Abstract The goal of this paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov
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