Parameter estimation in switching stochastic models

Date

2004

Editor(s)

Advisor

Gürler, Ülkü

Supervisor

Co-Advisor

Co-Supervisor

Instructor

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Abstract

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.

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Book Title

Degree Discipline

Industrial Engineering

Degree Level

Doctoral

Degree Name

Ph.D. (Doctor of Philosophy)

Citation

Published Version (Please cite this version)

Language

English

Type