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

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.