Title : ( Lp Distance for kernel density estimator in length-biased data )
Authors: Vahid Fakoor , Raheleh Zamini ,
Full TextAbstract
In this article we prove a central limit theorem for the $L_p$ distance $I_{n}(p)=\int_{\mathbb{R}} {|f_{n}(x)-f(x)|}^{p} d\mu(x), 1\leq p<\infty,$ where $\mu$ is a weight function and $f_{n}$ is the kernel density estimator proposed by Jones(1991) for length-biased data. The approach is based on the invariance principle for the empirical processes proved by Horv\'{a}th (1985). We study the difference $I_{n}(p)$ with its approximation in terms of its rates of convergence to zero. We subsequently present a central limit theorem for approximation of $I_{n}(p)$.
Keywords
, Central limit theorem; Length, biased data; $L_{p}$ distance; Kernel density estimator.
@article{paperid:1059171,
author = {Fakoor, Vahid and Raheleh Zamini},
title = {Lp Distance for kernel density estimator in length-biased data},
journal = {Communications in Statistics - Theory and Methods},
year = {2016},
volume = {46},
number = {18},
month = {January},
issn = {0361-0926},
pages = {9247--9264},
numpages = {17},
keywords = {Central limit theorem; Length-biased data; $L_{p}$ distance; Kernel density estimator.},
}
%0 Journal Article
%T Lp Distance for kernel density estimator in length-biased data
%A Fakoor, Vahid
%A Raheleh Zamini
%J Communications in Statistics - Theory and Methods
%@ 0361-0926
%D 2016
