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Orthogonalized smoothing for rescaled spike and slab models

Hemant Ishwaran and Ariadni Papana

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Abstract

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review background theory and discuss applications of rescaled spike and slab models to prediction problems involving orthogonal polynomials. We first consider global smoothing and discuss potential weaknesses. Some of these deficiencies are remedied by using local regression. The local regression approach relies on an intimate connection between local weighted regression and weighted generalized ridge regression. An important implication is that one can trace the effective degrees of freedom of a curve as a way to visualize and classify curvature. Several motivating examples are presented.

Chapter information

Source
Bertrand Clarke and Subhashis Ghosal, eds., Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 267-281

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1209398474

Digital Object Identifier
doi:10.1214/074921708000000192

Mathematical Reviews number (MathSciNet)
MR2459230

Subjects
Primary: 62J07: Ridge regression; shrinkage estimators
Secondary: 62J05: Linear regression

Keywords
effective degrees of freedom penalization selective shrinkage

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Ishwaran, Hemant; Papana, Ariadni. Orthogonalized smoothing for rescaled spike and slab models. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 267--281, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000192. https://projecteuclid.org/euclid.imsc/1209398474


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