In parametric modelling, maximum likelihood estimation is in general most powerful, but model misspecification can result in seriously biased estimators. Nonparametric modelling makes no assumptions; however, it would pay a price on the variance side since there are more unknowns to be estimated. Even worse, when the dimension of the covariates is large, nonparametric modelling has the ''curse of dimensionality" problem. We develop a semiparametric model which has a wide range of applications. It copes with multiple covariates and adapts to dynamic structural changes well. The associated estimation problem is solved by a simple and effective two-step method. The proposed estimator of the parametric part has root-n convergence rate, and the estimator of the nonparametric part enjoys an adaptivity property. Data-driven bandwidth selection and model selection procedures are suggested.
A simulation study demonstrates the performance of the proposed methods. Finally, the proposed model is used to analyse the infant mortality data of China. This is a joint work with Wenyang Zhang and Lu-Hung Chen.