Trigonometric Maximum Likelihood Estimation and Application to the Analysis of Incomplete Survival Information
Abstract A procedure is derived for computing maximum likelihood estimates from the sample trigonometric moments. Several examples are given which demonstrate the convenience of this hybrid approach. The Zippin-Armitage method for dealing with incomplete survival information is generalized. A simple expression is obtained for the survival curve given nonparametric estimators of (1) the probability density of survival times for patients who have died, and (2) the probability density of known survival times for patients still alive. It is shown that this new estimator approaches the Kaplan-Meier product limit as the sample size approaches infinity.