On Parametric Random Truncation Models

This paper deals with the estimation of parametric survival function in the proportional hazards model with randomly truncated data. Asymptotic variances of several estimators of survival function are compared in the exponential case. In particular, the nonparametric product-limit estimator has unbounded asymptotic variance under the present model conditions. Also it is shown numerically that the parametric maximum likelihood estimator (MLE) of survival function asymptotically is more efficient than the semiparametric MLE. Extension to other distributions case is discussed.