Abstract
In this article, the maximum spacing (MSP) method is extended to continuous time Markov chains and semi-Markov processes and consistency of the MSP estimator is proved. For independent and identically distributed univariate observations the idea behind the MSP method is to approximate the Kullback–Leibler information so that each contribution is bounded from above. Following the same idea, the MSP function in this article is defined as an approximation of the relative entropy rate for semi-Markov processes and continuous time Markov chains. The MSP estimator is defined as the parameter value that maximizes the MSP function. Consistency of the MSP estimator is also studied when the assigned model is incorrect.
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