Empirical Cummulative Density Function from a Univariate Censored Sample

TL;DR

This paper introduces a new nonparametric estimator for the cumulative distribution function from censored data, which performs better than the Kaplan-Meier estimator especially in small samples.

Contribution

A novel nonparametric estimator for the distribution function from censored samples, independent of the censoring mechanism assumptions.

Findings

F_hat outperforms Kaplan-Meier in simulations

Accurately estimates F(tau) even with small samples

Works with exponential and lognormal distributions

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.