Open Access
VOL. 3 | 2008 Orthogonalized smoothing for rescaled spike and slab models
Hemant Ishwaran, Ariadni Papana

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 267-281 (2008) DOI: 10.1214/074921708000000192


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.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459230

Digital Object Identifier: 10.1214/074921708000000192

Primary: 62J07
Secondary: 62J05

Keywords: effective degrees of freedom , Penalization , selective shrinkage

Rights: Copyright © 2008, Institute of Mathematical Statistics

Back to Top