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 re-sponse 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.

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Researchers should cite this work as follows:

• Min Zhang; Dabao Zhang (2010), "Penalized orthogonal-components regression for large p small n data," http://ccehub.org/resources/287.

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1. Empirical Bayes thresholding
2. Latent-variable model
3. POCRE
4. Sparse predictors
5. Supervised dimension re- duction