Efficient estimation of adaptive varying-coefficient partially linear regression model

The adaptive varying-coefficient partially linear regression (AVCPLR) model is proposed by combining the nonparametric regression model and varying-coefficient regression model with different smoothing variables. It can be seen as a generalization of the varying-coefficient partially linear regression model, and it is also an example of a generalized structured model as defined by Mammen and Neilsen [Mammen, E., Nielsen, J.P., 2003. Generalised structured models. Biometrika 90, 551–566]. Based on the local linear technique and the marginal integrated method, the initial estimators of these unknown functions are obtained, each of which has big variance. To decrease the variances of these initial estimators, the one-step backfitting technique proposed by Linton [Linton, O.B., 1997. Efficient estimation of additive nonparametric regression models. Biometrika 82, 93–100] is used to obtain the efficient estimators of all unknown functions for the AVCPLR model, and their asymptotic normalities are studied. Two simulated examples are given to illustrate the AVCPLR model and the proposed estimation methodology.