Robust smooth-threshold estimating equations for generalized varying-coefficient partially linear models based on exponential score function

In this paper, we present a new efficient and robust estimation procedure for generalized varying coefficient partially linear models (GVCPLMs), where the nonparametric coefficients are approximated by polynomial splines. A bounded exponential score function with a tuning parameter γγ and leverage based weights are applied to the estimating equations for achieving robustness against outliers in both the response and covariates directions. Our motivation for the new estimation procedure is that it enables us to achieve better robustness and efficiency by selecting automatically the tuning parameter γγ using the observed data. The proposed estimator is as asymptotically efficient as the common quasi-likelihood estimator when there are no outliers. Moreover, an automatic variable selection procedure is developed to select significant parametric components for the GVCPLM based on robust smooth-threshold estimating equations. Simulations and a real data example are used to demonstrate the finite sample behavior of the proposed estimator.