Orthogonalized smoothing for rescaled spike and slab models

Details Orthogonalized smoothing for rescaled spike and slab models Orthogonalized smoothing for rescaled spike and slab models

2008-05-21

arxiv.org/abs/0805.3279v1

IMS Collections 2008, Vol. 3, 267-281

Statistics

Applications

Published in at http://dx.doi.org/10.1214/074921708000000192 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

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.

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