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dc.contributor.authorDai, Wenlin
dc.contributor.authorTong, Tiejun
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2021-07-06T13:41:20Z
dc.date.available2021-07-06T13:41:20Z
dc.date.issued2016
dc.identifier.issn1532-4435
dc.identifier.urihttp://hdl.handle.net/10754/670034
dc.description.abstractWe propose a simple framework for estimating derivatives without fitting the regression function in nonparametric regression. Unlike most existing methods that use the symmetric difference quotients, our method is constructed as a linear combination of observations. It is hence very flexible and applicable to both interior and boundary points, including most existing methods as special cases of ours. Within this framework, we define the variance-minimizing estimators for any order derivative of the regression function with a fixed bias-reduction level. For the equidistant design, we derive the asymptotic variance and bias of these estimators. We also show that our new method will, for the first time, achieve the asymptotically optimal convergence rate for difference-based estimators. Finally, we provide an effective criterion for selection of tuning parameters and demonstrate the usefulness of the proposed method through extensive simulation studies of the first- and second-order derivative estimators.
dc.description.sponsorshipThe authors thank the editor, the associate editor and the two referees for their constructive comments that led to a substantial improvement of the paper. The work of Wenlin Dai and Marc G. Genton was supported by King Abdullah University of Science and Technology (KAUST). Tiejun Tong’s research was supported in part by Hong Kong Baptist University FRG grants FRG1/14-15/044, FRG2/15-16/038, FRG2/15-16/019 and FRG2/14-15/084.
dc.rightsArchived with thanks to JOURNAL OF MACHINE LEARNING RESEARCH
dc.subjectLinear combination
dc.subjectNonparametric derivative estimation
dc.subjectNonparametric regression
dc.subjectOptimal sequence
dc.subjectTaylor expansion
dc.titleOptimal Estimation of Derivatives in Nonparametric Regression
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.identifier.journalJournal of Machine Learning Research
dc.identifier.wosutWOS:000391669500001
dc.eprint.versionPost-print
dc.identifier.volume17
kaust.personDai, Wenlin
kaust.personGenton, Marc G.


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