Conditional least squares estimation and design for continuous-time stochastic processes

Typescript (photocopy).In this dissertation conditional least-squares estimation is applied to sampled continuous-time stochastic processes. The properties of estimators are studied through a theoretical development of their asymptotic behavior as well as an empirical study of their finite sample properties. A major portion of the theoretical study concentrates on the stochastic structure of the sampled process. Under two distinct observational schemes a complete analysis of the stochastic properties of the sampled process is given. This includes a development of the Markov property and stationarity for renewal sampled Markov processes. For the theoretical study of the asymptotic properties of the estimators, strong laws and central limit theorems for functions of the sampled process are presented. This asymptotic theory is derived under two general assumptions on the continuous-time process. They are: stationarity and asymptotic stationarity. Several methodological developments of conditional least-squares are included and explored. These developments involve generalizations to vector-valued processes, sequential estimation and applications to the alternate observational schemes. The theoretical development of conditional least-squares is a study of the asymptotic properties (consistency and asymptotic normality) of the estimators for the above-mentioned generalizations, including a specific study of the asymptotics for several types of observational schemes under renewal sampling. Finally a simulation study is used to explore finite sample properties of the estimator under various situations of interest