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Asymptotic normality of nonparametric estimators under α-mixing condition

✍ Scribed by Eckhard Liebscher

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
103 KB
Volume
43
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this paper we derive central limit theorems for three types of nonparametric estimators: kernel density estimators, Hermite series estimators and regression estimators. We assume that the sample is a part of a stationary sequence satisfying an -mixing property. The proofs are based on a central limit theorem for -mixing triangular arrays in the paper by Liebscher [1996, Stochastics and Stochastics Rep. 59, 241-258].

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Let (X 1 , Y 1 ), (X 2 , Y 2 ), ..., be d+1 dimensional random vectors which are distributed as (X, Y). Let %(x) be the conditional median, that is, We consider the problem of estimating %(x) from the data (X 1 , Y 1 ), ..., (X n , Y n ) which are :-mixing dependence. L 1 -norm kernel estimators of