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Abstract:
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We propose a new term semi-standard partial covariance (SPAC) which is better at distinguishing signals from noise than partial correlation. To select important predictors for highly correlated data, we propose to penalizes the SPACs instead of coefficients or partial correlations in penalty-based approaches like the Lasso. Under a Transformed Strong Irrepresentable Condition, the proposed method with Lasso penalty (SPAC-Lasso) has strongly sign consistency in both low-dimensional and high-dimensional settings. The Transformed Irrepresentable conditions includes cases where the Lasso is not consistent. The SPAC penalization method also improves performance of adaptive Lasso and SCAD penalties for highly correlated data, especially in high-dimensional settings. We apply simulations and a gene data set from the international 'HapMap' project to illustrate the proposed method.
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