MAXIMUM-LIKELIHOOD-ESTIMATION FOR GENERALIZED SEMI-MARKOV PROCESSES

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 proper ties (e.g., consistency, asymptotic normality, etc.), maximum likeliho od estimation is considered here. Under reasonable conditions on the p rocess, we show that a maximum likelihood estimator exists, and that i t converges to the true parameter at rate t(-1/2), where t is the leng th of the observation period. A related estimator, which is typically easier to compute, is also introduced. We show that the use of this es timator results in no loss of statistical efficiency. It is also shown that the estimation problem does decouple into separate subproblems w hen the process' transition probabilities and event distributions depe nd on different parameters.