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Adaptive weighting for flexible estimation in nonparametric regression models.


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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Title: Adaptive weighting for flexible estimation in nonparametric regression models.
Author: Nosedal-Sanchez, Alvaro
Advisor(s): Storlie, Curtis
Committee Member(s): Christensen, Ronald
Bedrick, Edward
Huerta, Gabriel
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject: Spatially Adaptive Smoothing
Nonparametric Regression
Regularization Method
Smoothing Spline
LC Subject(s): Smoothing (Statistics)
Estimation theory.
Regression analysis.
Nonparametric statistics.
Degree Level: Doctoral
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.
Graduation Date: May 2011
URI: http://hdl.handle.net/1928/12844

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