Robust statistical inference for varying-coefficient partially linear instrumental variable model based on modal regression

We study the variable selection for varying-coefficient partially linear model with some endogenous covariates. Combining instrumental variable adjustment technology and modal regression, we develop an efficient and robust variable selection procedure for selecting significant parametric and nonparametric components simultaneously, estimating the parameter and nonparametric function consistently. The proposed procedure can attenuate the effect of the endogenous variables, and is robust against outliers or heavy-tail error distributions. With appropriate selection of the tuning parameters, certain asymptotic properties of the resulting estimators are established. Moreover, the bandwidth selection and estimation algorithm for the proposed procedure are discussed. Some simulation results and a real example confirm that the performance of our procedure in finite samples is satisfactory.