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Penalized Orthogonal-Components Regression for Large p Small n Data
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.Comment: 12 page
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