Asymptotic expansion for ISE of kernel density estimators under censored dependent model

Vahid Fakoor, Sarah Jomhoori and Hasanali Azarnoosh

Statistics & Probability Letters, 2009, vol. 79, issue 17, 1809-1817

Abstract: In some long term studies, we encounter a series of dependent and censored observations. Randomly censored data consist of i.i.d. pairs of observations (Xi,[delta]i)i=1,...,n. If [delta]i=0, Xi denotes a censored observation, and if [delta]i=1, Xi denotes a survival time, which is the variable of interest. One of the global stochastic measures of the distance between a density and its kernel density estimator is integrated square error. In this paper, we apply the technique of strong approximation to establish an asymptotic expansion for the integrated square error of the kernel density estimate, when censored data are showing some kind of dependence.

Date: 2009
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