An approximate likelihood procedure for censored data

An approximate likelihood procedure is suggested for the estimation of the parameters of the density of a single homogeneous sample subject to right censoring. Two examples are given involving the gamma distribution. The method is typically consistent and although it is always inefficient, the efficiency loss is second-order in the degree of censoring when this is small. The relation of the techniques to the results of Reid (1981, Annals of Statistics 9, 78-92) on influence functions for censored data, to the EM algorithm, and to the nonparametric regression techniques of Miller (1976, Biometrika 63, 449-464) and Buckley and James (1979, Biometrika 66, 429-436) are indicated. Simple estimates of standard error are obtained.