Optimal difference-based estimation for partially linear models

Handle URI:
http://hdl.handle.net/10754/626605
Title:
Optimal difference-based estimation for partially linear models
Authors:
Zhou, Yuejin ( 0000-0002-0057-793X ) ; Cheng, Yebin; Dai, Wenlin; Tong, Tiejun
Abstract:
Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Zhou Y, Cheng Y, Dai W, Tong T (2017) Optimal difference-based estimation for partially linear models. Computational Statistics. Available: http://dx.doi.org/10.1007/s00180-017-0786-3.
Publisher:
Springer Nature
Journal:
Computational Statistics
Issue Date:
16-Dec-2017
DOI:
10.1007/s00180-017-0786-3
Type:
Article
ISSN:
0943-4062; 1613-9658
Sponsors:
Yuejin Zhou’s research was supported in part by the Natural Science Foundation of Anhui Grant (No. KJ2017A087), and the National Natural Science Foundation of China Grant (No. 61472003). Yebin Cheng’s research was supported in part by the National Natural Science Foundation of China Grant (No. 11271241). Tiejun Tong’s research was supported in part by the Hong Kong Baptist University Grants FRG1/16-17/018 and FRG2/16-17/074, and the National Natural Science Foundation of China Grant (No. 11671338).
Additional Links:
https://link.springer.com/article/10.1007%2Fs00180-017-0786-3
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZhou, Yuejinen
dc.contributor.authorCheng, Yebinen
dc.contributor.authorDai, Wenlinen
dc.contributor.authorTong, Tiejunen
dc.date.accessioned2018-01-01T12:19:02Z-
dc.date.available2018-01-01T12:19:02Z-
dc.date.issued2017-12-16en
dc.identifier.citationZhou Y, Cheng Y, Dai W, Tong T (2017) Optimal difference-based estimation for partially linear models. Computational Statistics. Available: http://dx.doi.org/10.1007/s00180-017-0786-3.en
dc.identifier.issn0943-4062en
dc.identifier.issn1613-9658en
dc.identifier.doi10.1007/s00180-017-0786-3en
dc.identifier.urihttp://hdl.handle.net/10754/626605-
dc.description.abstractDifference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.en
dc.description.sponsorshipYuejin Zhou’s research was supported in part by the Natural Science Foundation of Anhui Grant (No. KJ2017A087), and the National Natural Science Foundation of China Grant (No. 61472003). Yebin Cheng’s research was supported in part by the National Natural Science Foundation of China Grant (No. 11271241). Tiejun Tong’s research was supported in part by the Hong Kong Baptist University Grants FRG1/16-17/018 and FRG2/16-17/074, and the National Natural Science Foundation of China Grant (No. 11671338).en
dc.publisherSpringer Natureen
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs00180-017-0786-3en
dc.subjectAsymptotic normalityen
dc.subjectDifference-based methoden
dc.subjectDifference sequenceen
dc.subjectLeast squares estimatoren
dc.subjectPartially linear modelen
dc.titleOptimal difference-based estimation for partially linear modelsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalComputational Statisticsen
dc.contributor.institutionSchool of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Chinaen
dc.contributor.institutionSchool of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Chinaen
dc.contributor.institutionGlorious Sun School of Business and Management, Donghua University, Shanghai, Chinaen
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Kowloon, Chinaen
kaust.authorDai, Wenlinen
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