Acta mathematica scientia, Series B >
MODERATE DEVIATIONS AND LARGE DEVIATIONS FOR A TEST OF SYMMETRY#br# BASED ON KERNEL DENSITY ESTIMATOR
Received date: 2005-09-15
Revised date: 2006-10-08
Online published: 2008-07-20
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in <b>R</b>. The goal of this article is to prove moderate deviations and large deviations for the statistic
$\sup\limits_{x\in{{\Bbb R}}}| {f_{n}(x)-f_{n}(-x)}| $.
Key words： Symmetry test; kernel estimator; moderate deviations; large deviations
He Xiaoxia , Gao Fuqing . MODERATE DEVIATIONS AND LARGE DEVIATIONS FOR A TEST OF SYMMETRY#br# BASED ON KERNEL DENSITY ESTIMATOR[J]. Acta mathematica scientia, Series B, 2008 , 28(3) : 665 -674 . DOI: 10.1016/S0252-9602(08)60068-5
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