On the Optimal Non-Convexity of Penalty in Sparse Regression Models

In high-dimensionality regression modelling, the number of candidate covariates to be included in the predictor is quite large, and variable selection is critical. In this paper, we study in detail the CDF penalty, an adaptive non-convex penalty function that ensures consistent variable selection, along with unbiasedness and uniqueness of the solution. We evaluate the effect of the scale parameter in the CDF penalty on the estimates by stressing the role of the ratio between the number of observations and the number of variables.