Development of Specific hypothesis tests for estimated markov chains

We develop and evaluate the validity and power of two specific tests for the transition probabilities in a Markov chain estimated from aggregate frequency data. The two null hypotheses considered are (1) constancy of the diagonal elements of the one-step transition probability matrix and (2) an arbitrarily chosen transition probability’s being equal to a specific value. The formation of tests uses a general framework for statistical inference on estimated Markov processes; we also indicate how this framework can be used to form tests for a variety of other hypotheses. The validity and power performance of the two tests formed in this paper are examined in factorially designed Monte Carlo experiments. The results indicate that the proposed tests lead to type I error probabilities which are close to the desired levels and to high power against even small deviations from the null hypotheses considered.

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