Nonconvex penalized ridge estimations for partially linear additive models in ultrahigh dimension

Abstract

Nonconvex penalties (such as the smoothly clipped absolute deviation penalty and the minimax concave penalty) have some attractive properties including the 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 selection property of the NPR estimator for high-dimensional partially linear additive models with highly correlated predictors, where the dimensionality of covariates $p_n$ is allowed to increase exponentially with the sample size $n$. Simulation studies and a real data analysis are carried out to show the performance of the NPR method.