Penalized robust estimating equation and variable selection in a partially linear single-index varying-coefficient model

This paper focuses on the variable selection and estimation for a partially linear single-index varying-coefficient model. A novel fusing L 1 and exponential integral penalty and a new loss function are proposed to construct the penalized robust estimating equation (PREE) for variable selection and estimations of the regression parameters. The consistency of the variable selection procedure and the oracle property of the regularized estimators are proved under some regularity conditions. The bias correction technique is employed in PREE to avoid undersmoothing of the coefficient functions. An iteration algorithm is proposed for estimating the regression parameters. The finite sample performance of our method is validated through simulation studies, and a real data analysis further confirms the validity of the proposed method.