Robust group non-convex estimations for high-dimensional partially linear models

Abstract

High-dimensional data with a group structure of variables arise always in many contemporary statistical modelling problems. Heavy-tailed errors or outliers in the response often exist in these data. We consider robust group selection for partially linear models when the number of covariates can be larger than the sample size. The non-convex penalty function is applied to achieve both goals of variable selection and estimation in the linear part simultaneously, and we use polynomial splines to estimate the nonparametric component. Under regular conditions, we show that the robust estimator enjoys the oracle property. Simulation studies demonstrate the performance of the proposed method with samples of moderate size. The analysis of a real example illustrates that our method works well.