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dc.contributor.authorNosedal-Sanchez, Alvaro
dc.date.accessioned2011-07-02T16:06:16Z
dc.date.available2011-07-02T16:06:16Z
dc.date.issued2011-07-02
dc.date.submittedMay 2011
dc.identifier.urihttp://hdl.handle.net/1928/12844
dc.description.abstractWe propose a new method to find spatially adaptive smoothing splines. This new method breaks down the interval [0, 1] into p disjoint sub-intervals. Then we define p functional components in [0, 1], which have two important features. First, the purpose of each of these p components is to estimate the true function locally, i.e., in only one of the sub-intervals. Second, even though all components are defined on the entire domain, i.e. [0, 1], a component has curvature only in one of the aforementioned intervals. The p local estimates are then added together to produce a function estimate over the entire [0, 1] interval. In the proposed method, the additional flexibility that comes from finding these p local functional estimates does not come at any additional computational cost. In spite of having p components there is no need to specify (e.g., choose via cross validation) p smoothing parameters. Theory from COmponent Selection and Shrinkage Operator (COSSO), reduces the problem of specifying these p smoothing parameters to specifying only one smoothing parameter without a loss in flexibility. In fact, empirical studies indicate superior performance of COSSO in the additive model framework over that for the traditional additive model.en_US
dc.description.sponsorshipCONACYTen_US
dc.language.isoen_USen_US
dc.subjectSpatially Adaptive Smoothingen_US
dc.subjectNonparametric Regressionen_US
dc.subjectRegularization Methoden_US
dc.subjectSmoothing Splineen_US
dc.subject.lcshSmoothing (Statistics)
dc.subject.lcshEstimation theory.
dc.subject.lcshRegression analysis.
dc.subject.lcshNonparametric statistics.
dc.titleAdaptive weighting for flexible estimation in nonparametric regression models.en_US
dc.typeDissertationen_US
dc.description.degreeStatisticsen_US
dc.description.levelDoctoralen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorStorlie, Curtis
dc.description.committee-memberChristensen, Ronald
dc.description.committee-memberBedrick, Edward
dc.description.committee-memberHuerta, Gabriel
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