Statistica Sinica
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Partial correlation based variable selection method was proposed for normal linear regression models by Bühlmann, Kalisch and Maathuis (2010) as a comparable alternative method to regularization methods for variable selection. This paper addresses two important issues related to partial correlation based variable selection method: (a) whether this method is sensitive to normality assumption, and (b) whether this method is valid when the dimension of predictor increases in an exponential rate of the sample size. To address issue (a), we systematically study this method for elliptical linear regression models. ⋯ Since the TPC procedure includes the original proposal as a special case, our theoretical results address the issue (b) directly. As a by-product, the sure screening property of the first step of TPC was obtained. The numerical examples also illustrate that the TPC is competitively comparable to the commonly-used regularization methods for variable selection.