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 l
✦ LIBER ✦
The consistency and asymptotic normality of nearest neighbor density estimator under α-mixing condition
✍ Scribed by Liu Yanyan; Zhang Yanli
- Book ID
- 108422405
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 189 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0252-9602
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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