Maximum likelihood estimation for generalized semi-markov processes

Abstract

Parametric statistical inference for generalized semi-Markov processes is addressed. This class of processes encompasses a large number of “real-world” discrete-event stochastic systems. Because of its properties (e.g., consistency, asymptotic normality, etc.), maximum likelihood estimation is considered here. Under reasonable conditions on the process, we show that a maximum likelihood estimator exists, and that it converges to the true parameter at ratet ^−1/2, wheret is the length of the observation period. A related estimator, which is typically easier to compute, is also introduced. We show that the use of this estimator results in no loss of statistical efficiency. It is also shown that the estimation problem does decouple into separate subproblems when the process' transition probabilities and event distributions depend on different parameters.