Publication Date

7-2-2011

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.

Degree Name

Statistics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Advisor

Storlie, Curtis

First Committee Member (Chair)

Christensen, Ronald

Second Committee Member

Bedrick, Edward

Third Committee Member

Huerta, Gabriel

Project Sponsors

CONACYT

Language

English

Keywords

Smoothing (Statistics), Estimation theory, Regression analysis, Nonparametric statistics.

Document Type

Dissertation

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