Parametric estimation for randomly censored autocorrelated data.

This thesis is mainly concerned with the estimation of parameters in autoregressive models with censored data. For convenience, attention is restricted to the first-order stationary autoregressive (AR(1)) model in which the response random variables are subject to right-censoring. In their present form, currently available methods of estimation in regression analysis with censored autocorrelated data, which includes the MLE, are applicable only if the errors of the AR component of the model are Gaussian. Use of these methods in AR processes with non-Gaussian errors requires, essentially, rederivations of the estimators. Hence, in this thesis, we propose new estimators which arerobust in the sense that they can be applied with minor or no modifications to AR models with non-Gaussian. We propose three estimators, two of which the form of the distribution of the errors needs to be specified. The third estimator is a distribution-free estimator. As the reference to this estimator suggests, it is free from distributional assumptions in the sense that the error distribution is calculated from the observed data. Hence, it can be used in a wide variety of applications.In the first part of the thesis, we present a summary of the various currently available estimators for the linear regression model with censored independent and identically distributed (i.i.d.) data. In our review of these estimators, we note that the linear regression model with censored i.i.d. data has been studied quite extensively. Yet, use of autoregressive models with censored data has received very little attention. Hence, the remainder of the thesis focuses on the estimation of parameters for censored autocorrelated data. First, as part of the study, we review currently available estimators in regression with censored autocorrelated data. Then we present descriptions of the new estimators for censored ++