A bootstrap approximation to Lp_statistic of kernel density estimator in length-biased model

TL;DR

This paper develops a bootstrap method to approximate the distribution of the Lp_statistic for kernel density estimators in length-biased models, facilitating statistical inference in various applied fields.

Contribution

It establishes a bootstrap central limit theorem for the Lp_statistic in length-biased models, extending bootstrap theory to this context.

Findings

Bootstrap approximation is consistent for the Lp_statistic.

Theoretical validation of the bootstrap CLT in length-biased models.

Applicable to survival analysis and physics data.

Abstract

This article presents a bootstrap approximation to the Lp_statistics of kernel density estimator in length-biased model. Length-biased data arise in many situations, such as survival analysis, renewal processes and physics. The article establishes a bootstrap central limit theorem for the corresponding bootstrap version of this Lp_statistic. The bootstrap is a widely used tool in statistics and, therefore, the properties of this bootstrap approximation are of great interest in applied as well as in theoretical statistics.