Kernel density estimation with doubly truncated data

Abstract

In some applications with astronomical and survival data, doubly truncated data are sometimes encountered. In this work we introduce kernel-type density estimation for a random variable which is sampled under random double truncation. Two different estimators are considered. As usual, the estimators are defined as a convolution between a kernel function and an estimator of the cumulative distribution function, which may be the NPMLE [2] or a semiparametric estimator [9]. Asymptotic properties of the introduced estimators are explored. Their finite sample behaviour is investigated through simulations. Real data illustration is included.