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We propose a penalized orthogonal-components regression (POCRE) for large psmall n data. Orthogonal components are sequentially constructed to maximize,upon standardization, their correlation to the response residuals. A newpenalization framework, implemented via empirical Bayes thresholding, ispresented to effectively identify sparse predictors of each component. POCRE iscomputationally efficient owing to its sequential construction of leadingsparse principal components. In addition, such construction offers otherproperties such as grouping highly correlated predictors and allowing forcollinear or nearly collinear predictors. With multivariate responses, POCREcan construct common components and thus build up latent-variable models forlarge p small n data.

Penalized Orthogonal-Components Regression for Large p Small n Data