Abstract
Multiplying factors are presented which substantially increase 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.
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