Combination of Nonconvex Penalties and Ridge Regression for High-Dimensional Linear Models

Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression(abbreviated as NPR), we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates pn is allowed to increase exponentially with the sample size n. Simulation studies and a real data example are presented to verify the performance of the NPR method.