Title : ( A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model )
Authors: Petros Asghari , Vahid Fakoor , Majid Sarmad ,
Full TextAbstract
In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum ( Y ) is randomly left truncated and it is sampled if Y ≥ T , where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n^1 / 6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.
Keywords
, Asymptotic normality, Berry-Esseen, kernel density estimation, rate of convergence, left-truncation
@article{paperid:1041676,
author = {Asghari, Petros and Fakoor, Vahid and Sarmad, Majid},
title = {A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model},
journal = {Communications for Statistical Applications and Methods},
year = {2014},
volume = {21},
number = {2},
month = {April},
issn = {2287-7843},
pages = {115--124},
numpages = {9},
keywords = {Asymptotic normality; Berry-Esseen; kernel density estimation; rate of convergence; left-truncation},
}
%0 Journal Article
%T A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model
%A Asghari, Petros
%A Fakoor, Vahid
%A Sarmad, Majid
%J Communications for Statistical Applications and Methods
%@ 2287-7843
%D 2014
