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Adaptive weighting for flexible estimation in nonparametric regression models.

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/12844

Adaptive weighting for flexible estimation in nonparametric regression models.

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dc.contributor.author Nosedal-Sanchez, Alvaro
dc.date.accessioned 2011-07-02T16:06:16Z
dc.date.available 2011-07-02T16:06:16Z
dc.date.issued 2011-07-02
dc.date.submitted May 2011
dc.identifier.uri http://hdl.handle.net/1928/12844
dc.description.abstract We 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.sponsorship CONACYT en_US
dc.language.iso en_US en_US
dc.subject Spatially Adaptive Smoothing en_US
dc.subject Nonparametric Regression en_US
dc.subject Regularization Method en_US
dc.subject Smoothing Spline en_US
dc.subject.lcsh Smoothing (Statistics)
dc.subject.lcsh Estimation theory.
dc.subject.lcsh Regression analysis.
dc.subject.lcsh Nonparametric statistics.
dc.title Adaptive weighting for flexible estimation in nonparametric regression models. en_US
dc.type Dissertation en_US
dc.description.degree Statistics en_US
dc.description.level Doctoral en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Storlie, Curtis
dc.description.committee-member Christensen, Ronald
dc.description.committee-member Bedrick, Edward
dc.description.committee-member Huerta, Gabriel


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