Kernel density estimation with doubly truncated data. (English) Zbl 1274.62271
Summary: 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 or a semiparametric estimator. Asymptotic properties of the introduced estimators are explored. Their finite sample behaviour is investigated through simulations. Real data illustration is included.
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