Bandwidth selection for kernel density estimation with length-biased   data
  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. 
Mar\'ia Isabel Borrajo, Wenceslao Gonz\'alez-Manteiga and Mar\'ia   Dolores Mart\'inez-Miranda
stat.ME stat.CO