PARAMETER ESTIMATION IN SWITCHING STOCHASTIC MODELS GÜLDAL GÜLERYÜZ Ph.D. in Industrial Engineering Supervisor: Prof. Dr. Ülkü Gürler May, 2004 In this thesis, we suggest an approach to statistical parameter estimation when an estimator is constructed by the trajectory observations of a stochastic system and apply the approach to reliability models. We analyze the asymptotic properties of the estimators constructed by the trajectory observations using moments method, maximum likelihood method and least squares method. Using limit theorems for Switching Processes and the results for parameter estimation by trajectory observations, we study the behavior of moments method estimators which are constructed by the observations of a trajectory of a switching process and prove the consistency and asymptotic normality of such estimators. We consider four different reliability models with large number of devices. For each of the models, we represent the system process as a Switching Process and prove that the system process converges to the solution of a differential equation. We also prove the consistency of the moments method estimators for each model. Simulation results are also provided to support asymptotic results and to indicate the applicability of the approach to finite sample case for reliability models.

Parameter estimation in switching stochastic models

A new approach is proposed to problems of asymptotic parameter estimation in stochastic switching systems. In this approach, results on the asymptotic behavior of solutions of stochastic equations and theorems of the type of averaging are used for switching processes. This approach allows one to investigate asymptotic properties of estimates of parameters constructed from observed trajectories for a numerous class of stochastic systems with regular behaviors of trajectories under stationary and transient conditions.

G. Guleryuz

Papers

Statistical Estimation of Switching Systems under Transient Conditions and Applications in Reliability Models