Kybernetika 62 no. 4, 643-674, 2026

Asymptotic normality of kernel estimators under censoring and association

Mohamed Boukeloua, Sarra Leulmi and Ferial SaihiDOI: 10.14736/kyb-2026-4-0643

Abstract:

In this work, we study kernel estimators of the density and the failure rate in the context of association and twice censoring. Association is a very interesting type of dependence given the fact that it covers many useful random processes. In this context, we assume that we have at disposal a sample of strictly stationary and associated copies of the variable of interest. Furthermore, this variable is right censored by another variable, the minimum of the two variables is left censored and the three latent variables are independent. Under these assumptions, we establish the asymptotic normality of kernel estimators of the density and the failure rate. Then, we illustrate the performance and the Gaussian behavior of these estimators through a simulation study. The results of this study show the good quality of estimation and the good behavior of the studied asymptotic distributions with respect to the standard normal distribution. We also show the performance of our estimators using an application on a real data set.

Keywords:

asymptotic normality, density, twice censoring, associated data, kernel estimators, failure rate

Classification:

62N02, 62G07, 62G20

paper.pdf

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