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dc.contributor.authorDai, Wenlin
dc.contributor.authorTong, Tiejun
dc.contributor.authorZhu, Lixing
dc.date.accessioned2017-10-01T05:07:27Z
dc.date.available2017-10-01T05:07:27Z
dc.date.issued2017-09-01
dc.identifier.citationDai W, Tong T, Zhu L (2017) On the Choice of Difference Sequence in a Unified Framework for Variance Estimation in Nonparametric Regression. Statistical Science 32: 455–468. Available: http://dx.doi.org/10.1214/17-STS613.
dc.identifier.issn0883-4237
dc.identifier.doi10.1214/17-STS613
dc.identifier.urihttp://hdl.handle.net/10754/625520
dc.description.abstractDifference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this paper, we propose a unified framework for variance estimation that combines the linear regression method with the higher-order difference estimators systematically. The unified framework has greatly enriched the existing literature on variance estimation that includes most existing estimators as special cases. More importantly, the unified framework has also provided a smart way to solve the challenging difference sequence selection problem that remains a long-standing controversial issue in nonparametric regression for several decades. Using both theory and simulations, we recommend to use the ordinary difference sequence in the unified framework, no matter if the sample size is small or if the signal-to-noise ratio is large. Finally, to cater for the demands of the application, we have developed a unified R package, named VarED, that integrates the existing difference-based estimators and the unified estimators in nonparametric regression and have made it freely available in the R statistical program http://cran.r-project.org/web/packages/.
dc.description.sponsorshipTiejun Tong's research was supported by the National Natural Science Foundation of China grant (No. 11671338), and the Hong Kong Baptist University grants FRG1/14-15/044, FRG2/15-16/019 and FRG2/15-16/038. Lixing Zhu's research was supported by the Hong Kong Research Grants Council grant (No. HKBU202810). The authors thank the editor, the associate editor and two reviewers for their constructive comments that have led to a substantial improvement of the paper.
dc.publisherInstitute of Mathematical Statistics
dc.relation.urlhttps://projecteuclid.org/euclid.ss/1504253126
dc.rightsArchived with thanks to Statistical Science
dc.subjectDifference-based estimator
dc.subjectnonparametric regression
dc.subjectoptimal difference sequence
dc.subjectordinary difference sequence
dc.subjectresidual variance
dc.titleOn the Choice of Difference Sequence in a Unified Framework for Variance Estimation in Nonparametric Regression
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalStatistical Science
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, , Hong Kong
kaust.personDai, Wenlin
refterms.dateFOA2018-06-13T19:11:07Z


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