A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors-Reference-Cited by-同舟云学术

A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors

Published:2019-12-01 Issue:6 Volume:69 Page:1471-1484
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Ding Liwang¹²,Chen Ping¹

Affiliation:

1. School of Science , Nanjing University of Science and Technology , Xiaolingwei Street 200 , Nanjing , 210094 , China

2. School of Information and Statistics , Guangxi University of Finance and Economics , Mingxiu West Road 100 , Nanning , 530003 , China

Abstract

Abstract In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0323/pdf

Reference29 articles.

1. Antoniadis, A.—Grégoire, G.—Mckeague, I. W.: Wavelet methods for curve estimation, J. Amer. Statist. Assoc. 89 (1994), 1340–1352.

2. Chen, W.—Wang, Y. B.—Cheng, D. Y.: An inequality of widely dependent random variables and its applications, Lith. Math. J. 56 (2016), 16–31.

3. Deng, X.—Wang, X. J.: Asymptotic property of M estimator in classical linear models under dependent random errors, Methodol. Comput. Appl. Probab. 20 (2018), 1069–1090.

4. Ding, L. W.—Chen, P.—Li, Y. M.: Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples, Statist. Papers (2018), 10.1007/s00362-018-1050-9.

5. Ding, L. W.—Chen, P.—Li, Y. M.: Berry-Esseen bound of wavelet estimators in heteroscedastic regression model with random errors, Int. J. Comput. Math. 96 (2019), 821–852.

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