Değişen stokastik modellerde parametre tahminlemesi

ABSTRACTPARAMETER ESTIMATION IN SWITCHINGSTOCHASTIC MODELSü ü üGULDAL GULERYUZPh.D. in Industrial EngineeringüuuSupervisor: Prof. Dr. Ulkü GürlerMay, 2004In this thesis, we suggest an approach to statistical parameter estimationwhen an estimator is constructed by the trajectory observations of a stochasticsystem and apply the approach to reliability models. We analyze the asymptoticproperties of the estimators constructed by the trajectory observations using mo-ments method, maximum likelihood method and least squares method. Usinglimit theorems for Switching Processes and the results for parameter estimationby trajectory observations, we study the behavior of moments method estimatorswhich are constructed by the observations of a trajectory of a switching processand prove the consistency and asymptotic normality of such estimators. We con-sider four different reliability models with large number of devices. For each of themodels, we represent the system process as a Switching Process and prove thatthe system process converges to the solution of a differential equation. We alsoprove the consistency of the moments method estimators for each model. Simu-lation results are also provided to support asymptotic results and to indicate theapplicability of the approach to finite sample case for reliability models.Keywords: Parameter estimation, Switching Processes, Reliability models.iv