| In this dissertation, we propose a flexible semi-parametric model called additive coefficient model (ACM). In the ACM, one assumes that the response depends linearly on some covariates, whose regression coefficients, however, are additive functions of another set of covariates. The ACM can be viewed as a generalization of the classic linear models in the sense that instead of assuming the coefficients to be constants like the linear model does, it allows the regression coefficients to vary with another set of covariates through an additive function form.;This dissertation focuses on the estimation of the ACM. Two different approaches are considered. One is the local polynomial based marginal integration method, and the other one is the polynomial spline estimation. The local polynomial smoothing is local in nature, whereas the polynomial spline is a global smoothing method. This difference, in turn, leads to the difference in the asymptotic behavior of the two types of estimators.;Under weak dependence, the point-wise asymptotic normality is established for the marginal integration estimators. It is found that the estimators of the parameters in the regression coefficients have rate of convergence 1/ n , and the nonparametric additive components are estimated at the same rate of convergence as in univariate smoothing. In contrast, only mean square convergence is established for the polynomial spline estimators. However, the polynomial spline method is much simpler in both computation and inference. The nonparametric versions of AIC and BIC are adopted easily based on polynomial spline estimation, for the model selection purpose.;Monte Carlo studies are conducted to compare the numerical performances of the two estimation methods, as well as the model selection procedures. The simulation studies show that besides being highly efficient in terms of computing, the polynomial spline estimators are also more accurate than or at least as good as the local polynomial based estimators. The ACM is also successfully applied to several interesting empirical examples: West German GNP, Housing price, and Sunspot data, where the semi-parametric additive coefficient model demonstrates superior performance in terms of out-of-sample forecasts. |
