%0 Journal Article
%T A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
%J Journal of Sciences, Islamic Republic of Iran
%I University of Tehran
%Z 1016-1104
%A Asghari, P.
%A Fakoor, V.
%A Sarmad, M.
%D 2015
%\ 09/01/2015
%V 26
%N 3
%P 265-272
%! A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
%K Asymptotic normality
%K Berry-Esseen theorem
%K Kernel estimator
%K Rate of convergence
%K Length-biased
%R
%X 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.
%U https://jsciences.ut.ac.ir/article_55314_84b4409865483c3736c46be5ce3efb54.pdf