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2009 Penalized orthogonal-components regression for large p small n data
Dabao Zhang, Yanzhu Lin, Min Zhang
Electron. J. Statist. 3(none): 781-796 (2009). DOI: 10.1214/09-EJS354

Abstract

Here we propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data.

Citation

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Dabao Zhang. Yanzhu Lin. Min Zhang. "Penalized orthogonal-components regression for large p small n data." Electron. J. Statist. 3 781 - 796, 2009. https://doi.org/10.1214/09-EJS354

Information

Published: 2009
First available in Project Euclid: 11 August 2009

zbMATH: 1326.62149
MathSciNet: MR2534201
Digital Object Identifier: 10.1214/09-EJS354

Subjects:
Primary: 62J05
Secondary: 62H20, 62J07

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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