Estimation in generalised varying-coefficient models with unspecified link functions

In this paper, we study the generalised varying-coefficient models, where the link function is unspecified and the response variable can be either continuous or discrete. As the link function is unspecified, the models under investigation become unidentifiable. In this paper, we derive an identification condition for the generalised varying-coefficient models, which is much weaker and more reasonable than that given by Kuruwita et al. (2011) whose model can be seen as a special case of our modelling framework. Under the identification condition, we introduce a nonparametric iterative procedure to estimate the functional coefficient with its direction and norm as well as the unspecified link function, and then establish the asymptotic properties of the resulting nonparametric estimators. Furthermore, a weighted least squares based algorithm is provided to implement the iterative estimation procedure. The simulation studies and empirical application show that our estimation methodology works quite well in both small and median sample cases.