Estimating Mean and Variance From Right-censored Data

Estimation of the population mean and variance from (right) censored data has gained more interest recently in biomedical and engineering studies. The purpose of the paper is to introduce some new ideas, but also to give a fresh look at the past that can be of interest in teaching, using an elementary approach. A simple intuitive procedure of imputation of censored values for estimation of the mean and variance, inspired by mean remaining life, has been established, and can be easily performed using a convenient recursive calculation. This method is strongly connected with the definition of the Kaplan-Meier survival curve. Rationale behind the K-M “mysterious” estimator of the variance of the sample mean has been discussed in elementary terms. The recursive procedure has been further extended to these cases. An approach to a measure of the effect of censoring has been suggested.