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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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037837...

Related URL: http://dx.doi.org/10.1016/0378-3758(92)90002-A

## Abstract

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 T_{k} be the first hitting time of a state k. Given a realization {xj;0≤j≤n} of {Xj;0≤j≤n}, let P_{n} be the maximum likelihood estimate of P. In this paper, the distribution of the naive bootstrap of the pivot √n( P_{n}-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 |
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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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