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Biometrika 1975 62(3):595-598; doi:10.1093/biomet/62.3.595
© 1975 by Biometrika Trust
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Corrections to likelihood ratio tests of hypotheses concerning the parameters of Markov chains

STEPHEN A. SHARP

Department of Psychology, University of Liverpool

Multiplying factors are presented which substantially inorease the rate at which the likelihood ratio test statistic converges to its limiting chi-squared distribution as the number of observations increases. The corrections apply to the following hypotheses about Markov chain sequences: that the transition probabilities are stationary over time; that the chain is of a given order; and that several samples come from the same chain. Some technical features of the corrections are discussed and their applicability via computer programs is mentioned.

Key Words: Correction • Finite samples • Likelihood ratio • Markov chains


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