Robust variable selection for the varying index coefficient models

Recently, the statistical inference of the varying index coefficient model has been widely concerned. However, to the best of our knowledge, there has no existing robust variable selection method for the varying index coefficient model in the presence of outliers in the response and covariates. To overcome this difficulty, we develop a robust variable selection method for the varying index coefficient model via the exponential squared loss (ESL) function in this article. We first approximate nonparametric functions by B-spline basis functions and then apply the minorization-maximization (MM) algorithm and the Fisher scoring algorithm to calculate the proposed estimators. Under some mild conditions, the theoretical properties of the proposed estimators are established. Furthermore, we propose a data-driven procedure to select the tuning parameters. Some numerical simulations are conducted to illustrate the finite sample performance of the proposed method. Finally, the analysis of New Zealand workforce data reveals the merit of the proposed method.