In high-dimensional data settings, dimensionality reduction or variable selection are key steps when using statistical learning techniques. Principal Covariate Regression-type methods aim to perform both dimensionality reduction and (regularized) regression steps in one analysis. However, existing PCovR methods cannot simultaneously select dimensionalities and estimate regularized coefficients, forcing researchers to make ad-hoc choices in the order of these steps. In this study, we propose a novel method called Principal Covariate Regression with Nuclear Norm Penalty (PcovRnnp) that allows simultaneous dimension reduction and estimation of regularized coefficients.

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