Empirical Cummulative Density Function from a Univariate Censored Sample

Abstract

Let F be an unknown univariate distribution function to be estimated from a sample containing censored observations and tau be in dom(F). The author has derived a novel nonparametric estimator F_hat for F without making any assumptions regarding the nature of the censoring mechanism or the distribution function F. The distribution of F_hat(tau) can be easily and accurately estimated even for small sample sizes. The estimator F_hat has significantly outperformed the Kaplan Meier estimator in a simulation study with an exponential and a lognormal distribution functions F and a censoring mechanism defined by i.i.d. uniform random observation points.