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TESTING FOR REVERSIBILITY IN MARKOV CHAIN DATA

Published online by Cambridge University Press:  30 July 2012

Tara L. Steuber ,
Peter C. Kiessler  and
Robert Lund
Tara L. Steuber
Affiliation:
Department of Mathematical Sciences, Clemson University, O-106 Martin Hall, Clemson, SC 29634-0975 E-mails: tsteube@clemson.edu; kiesslp@clemson.edu; lund@clemson.edu
Peter C. Kiessler
Affiliation:
Department of Mathematical Sciences, Clemson University, O-106 Martin Hall, Clemson, SC 29634-0975 E-mails: tsteube@clemson.edu; kiesslp@clemson.edu; lund@clemson.edu
Robert Lund
Affiliation:
Department of Mathematical Sciences, Clemson University, O-106 Martin Hall, Clemson, SC 29634-0975 E-mails: tsteube@clemson.edu; kiesslp@clemson.edu; lund@clemson.edu
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Abstract

This paper introduces two statistics that assess whether (or not) a sequence sampled from a stationary time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 4 , October 2012 , pp. 593 - 611
Copyright
Copyright © Cambridge University Press 2012

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