Integrated square error of nonparametric estimators of regression function-Reference-Cited by-同舟云学术

Integrated square error of nonparametric estimators of regression function

Published:2023 Issue:27 Volume:37 Page:9391-9400
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Miao Yu¹,Ye Jun²,Zhang Wanyu³

Affiliation:

1. College of Mathematics and Information Science, Henan Normal University, Henan Province, China + Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Henan Province, China

2. College of Mathematics and Information Science, Henan Normal University, Henan Province, China

3. Department of Mathematical Sciences, University of Liverpool, Merseyside, L ZX, England

Abstract

In the present paper, we consider the nonparametric regression and study the integrated square error for nonparametric estimate of the unknown function. For the case that the errors of the regression model are martingale differences, the asymptotic normality and consistency of the integrated square error are established. These results improve the works in Ioannides [5].

Publisher

National Library of Serbia

Reference9 articles.

1. Y. S. Chow, H. Teicher, Probability Theory, (3rd edition), Springer, LLC, 1997.

2. P. Hall, Central limit theorem for integrated square error of multivariate nonparametric density estimators, J. Multivariate Anal. 14 (1984), 1-16.

3. P. Hall, Integrated square error properties of kernel estimators of regression functions, Ann. Statist. 12 (1984), 241-260.

4. P. Hall, C. C. Heyde, Martingale Limit Theory and its Application, Academic Press, New York (1980), P58.

5. D. A. Ioannides, Integrated square error of nonparametric estimators of regression function: The fixed design case, Statist. Probab. Lett. 15 (1992), 85-94.

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