Large-Sample Theory for Inference in Parametric Models

Asymptotic theory is essential for censored data analysis due to the typical absence of closed-formsolutions and exact distributions. This chapter discusses the asymptotic theory for parametric maximum likelihood estimators and their applications to confidence interval estimation and hypothesis testing. Although semiparametric inference based on partial likelihood under the Coxmodel is more commonly used, understanding parametric inference serves as a helpful precursor. Some of the procedures are illustrated using data from a recent large clinical trial. The numerical issues associated with Weibull regression are addressed, and parametric regression with the new model discussed in Chapter Three is demonstrated. Robust estimation is also briefly covered.