Robust variable selection for additive coefficient models

Abstract

Additive coefficient models generalize linear regression models by assuming that the relationship between the response and some covariates is linear, while their regression coefficients are additive functions. Because of its advantages in dealing with the “curse of dimensionality”, additive coefficient models gain a lot of attention. The commonly used estimation methods for additive coefficient models are not robust against high leverage points. To circumvent this difficulty, we develop a robust variable selection procedure based on the exponential squared loss function and group penalty for the additive coefficient models, which can tackle outliers in the response and covariates simultaneously. Under some regularity conditions, we show that the oracle estimator is a local solution of the proposed method. Furthermore, we apply the local linear approximation and minorization-maximization algorithm for the implementation of the proposed estimator. Meanwhile, we propose a data-driven procedure to select the tuning parameters. Simulation studies and an application to a plasma beta-carotene level data set illustrate that the proposed method can offer more reliable results than other existing methods in contamination schemes.