A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data

Asghari, P.; Fakoor, V.; Sarmad, M.

A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data

Document Type : Original Research Articles

Authors

P. Asghari

V. Fakoor

M. Sarmad

Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.

Abstract

Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infinity by a proper choice of the bandwidth.The results of a simulation study is also presented in this paper inorder to examine the performance of the result.

Keywords

Asymptotic normality

Berry-Esseen theorem

Kernel estimator

Rate of convergence

Length-biased