Variable Bandwidth Kernel Density Estimation for Censored Data

Abstract

It has long been recognized that accurate estimation of the density function is an important problem for inference with censored data (see Gehan, 1969). This paper presents a new kernel type estimator, which smooths at observed lifetimes inversely proportional to their density according to Abramson's square root law. It is shown that a similar reduction in bias is achieved.

Key Words:

• Censored data
• Density estimation
• Kaplan-Meier estimator
• Kernel Smoothing