Bandwidth selection for kernel density estimation with length-biased data

TL;DR

This paper investigates kernel density estimation for length-biased data, proposing bootstrap-based bandwidth selectors and a rule-of-thumb, with comparisons and simulations to evaluate their performance.

Contribution

It introduces two new bootstrap methods for bandwidth selection in kernel density estimation with length-biased data, enhancing existing techniques.

Findings

Bootstrap methods are consistent for bandwidth selection.

Proposed methods outperform cross-validation in simulations.

Rule-of-thumb provides a simple alternative with competitive performance.

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.