Bootstrapping Markov chains: countable case

Athreya, K. B. ; Fuh, C. D. (1992) Bootstrapping Markov chains: countable case Journal of Statistical Planning and Inference, 33 (3). pp. 311-331. ISSN 0378-3758

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Let X be an irreducible, aperiodic and positive recurrent Markov chain with a countably infinite state space S and transition probability matrix P. Let π be the stationary probability and Tk be the first hitting time of a state k. Given a realization {xj;0≤j≤n} of {Xj;0≤j≤n}, let Pn be the maximum likelihood estimate of P. In this paper, the distribution of the naive bootstrap of the pivot √n( Pn-P) is shown to appropriate that of the pivot as n→∞. The approach used is via a double array of Markov chains for which a weak law and a central limit theorem are established. Next, in order to estimate analogous quantities for the stationary probability and hitting time distribution, two different bootstrap methods are discussed.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Bootstrap Estimation; Hitting Times; Markov Chains; Stationary Distributions; Transition Probabilities
ID Code:1119
Deposited On:05 Oct 2010 12:54
Last Modified:12 May 2011 09:57

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