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dc.contributor.authorZhou, Yuejin
dc.contributor.authorCheng, Yebin
dc.contributor.authorDai, Wenlin
dc.contributor.authorTong, Tiejun
dc.date.accessioned2018-01-01T12:19:02Z
dc.date.available2018-01-01T12:19:02Z
dc.date.issued2017-12-16
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.
dc.identifier.issn0943-4062
dc.identifier.issn1613-9658
dc.identifier.doi10.1007/s00180-017-0786-3
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.
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).
dc.publisherSpringer Nature
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs00180-017-0786-3
dc.subjectAsymptotic normality
dc.subjectDifference-based method
dc.subjectDifference sequence
dc.subjectLeast squares estimator
dc.subjectPartially linear model
dc.titleOptimal difference-based estimation for partially linear models
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalComputational Statistics
dc.contributor.institutionSchool of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China
dc.contributor.institutionSchool of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China
dc.contributor.institutionGlorious Sun School of Business and Management, Donghua University, Shanghai, China
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Kowloon, China
kaust.personDai, Wenlin


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