Robust Variable Selection for the Varying Coefficient Partially Nonlinear Models

In this paper, we develop a robust variable selection procedure based on the exponential squared loss (ESL) function for the varying coefficient partially nonlinear model. Under certain conditions, some asymptotic properties of the proposed penalized ESL estimator are established. Meanwhile, the proposed procedure can automatically eliminate the irrelevant covariates, and simultaneously estimate the nonzero regression coefficients. Furthermore, we apply the local quadratic approximation (LQA) and minorization–maximization (MM) algorithm to calculate the estimates of non-parametric and parametric parts, and introduce a data-driven method to select the tuning parameters. Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset. Finally, we apply the proposed procedure to analyze the Boston housing price data. The results reveal that the proposed method has a better prediction ability.