Presmoothed kernel density estimator for censored data

Authors: Cao R.; Jácome M.A.

Source: Journal of Nonparametric Statistics, Volume 16, Numbers 1-2, Numbers 1-2/February-April 2004 2003 , pp. 289-309(21)

Publisher: Taylor and Francis Ltd

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Abstract:

Some kernel density estimator is presented in the context of right randomly censored data. The estimator makes use of presmoothing ideas replacing the indicators of no censoring by some preliminary nonparametric estimator of the conditional probability of uncensoring. Some i.i.d representation is given for this presmoothing estimator. This is useful to obtain the limit distribution and the asymptotic mean squared error of the estimator. An asymptotic mean integrated squared error result is also presented and used to derive large-sample formulas for the optimal presmoothing and the smoothing parameters. Finally, some simulations illustrate the theory.

Keywords: Bandwidth selection; Kaplan-Meier estimator; Mean integrated squared error; Nonparametric density estimator; Survival analysis

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10485250310001622622

Publication date: 2003-02-01