Relative density estimation for left truncated and right censored data

• Published in: Journal of nonparametric statistics Vol. 20; no. 8; pp. 693 - 720
• Main Authors: Molanes-López, Elisa-María, Cao, Ricardo
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.11.2008
• Subjects: i.i.d. representation; kernel estimator; optimal bandwidth; survival analysis; two-sample problem
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485250802447882

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.