Bandwidth selection for kernel density estimation with length-biased data. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Borrajo, M. I.; González-Manteiga, W.; Martínez-Miranda, M. D.
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 3(2017)
• Page Start: 636
• Page End: 668
• Publication Date: 2017-07-03
• Subjects: Bootstrap -- rule-of-thumb -- cross-validation -- nonparametric -- weighted data; 62G07 -- 62G09 -- 62G20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1339309
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples.