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Research Article

Asymptotic properties of asymmetric kernel estimators for non-negative and censored data

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Pages 2977-3004 | Received 21 Mar 2022, Accepted 17 Nov 2022, Published online: 29 Nov 2022
 

Abstract

Let {Xi,i1} be a sequence of independent and identically distributed random variables with distribution function F and probability density function f. We propose new type of kernel estimators for density and hazard functions that perform well at the boundary, when the variable of interest is positive and right censored. The estimators are constructed using asymmetric kernels with expectation 1. We establish uniform strong consistency rates and we study asymptotic properties and normality of the resulting estimators. A large simulation study is conducted to comfort the theoretical results. An application to real data is done.

Acknowledgement

The authors are indebted to an anonymous referee whose careful reading and constructive comments and suggestions helped to improve an earlier version of this paper.

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