4.1 Article

Relative density estimation for left truncated and right censored data

Journal

JOURNAL OF NONPARAMETRIC STATISTICS
Volume 20, Issue 8, Pages 693-720

Publisher

TAYLOR & FRANCIS LTD
DOI: 10.1080/10485250802447882

Keywords

i; i; d; representation; kernel estimator; optimal bandwidth; survival analysis; two-sample problem

Funding

  1. EU [BES-2003-1170, MTM2005-00429]
  2. XUGA [PGIDIT03PXIC10505-PN]

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In biostatistical applications, it is very common that the generation of data is subject to mechanisms of loss of information such as censoring and truncation. In this setting, the direct application of traditional methods designed for completely observed data is not suitable at all. In the setting of a two-sample problem, this paper is focused on a kernel-type relative density estimator defined for left truncated and right censored data. First of all, an asymptotic representation of the estimator is found and based on this representation, its bias, variance and limit distribution are obtained. Then, a plug-in global bandwidth selector is designed for the kernel-type relative density estimator and their performance is checked through a simulation study. Finally, the estimator and the bandwidth selector are applied to a medical data set concerning gastric adenocarcinoma.

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