本篇論文使用Seifert與Gasser (1996)的區域線性脊迴歸方法來估計同時具有多重線性迴歸式與無母數迴歸函數的半參數迴歸(semiparametric regression)模型，並利用交叉驗證法(cross validation)來選取最佳帶寬(bandwidth)和脊迴歸參數(ridge parameter)。根據模擬結果，當區域線性估計量和區域脊迴歸估計量均各自經由交叉驗證法選取其最適參數時，後者的無母數迴歸函數之估計式有明顯較小的樣本期望積分方差(sample mean integrated square error)並且其多重線性迴歸之參數估計式具有明顯較小的均方差(mean square error)。 In nonparametric regression analysis, local linear estimator (LLE) enjoys both smaller asymptotic bias and smaller asymptotic variance. However, Seifert and Gasser (1996) pointed out that in finite sample situations, when the design points are sparse or when design points are close to each other, LLE has unbounded conditional variance. The curve that estimated from the LLE has rough appearance accordingly; In order to improve this problem, Seifert and Gasser (1996) combines the local linear smoothing method and ridge regression to construct the local linear ridge regression estimator (LLRRE).
This thesis use local linear ridge regression method of Seifert and Gasser (1996) to improve the estimation of semiparametric regression which comprises both parametric and nonparametric regression component. A cross-validation method is used to select the optimal bandwidth and ridge regression parameters. According to the simulation results, when LLE and LLRRE both use their respective cross validated parameters, the LLRRE’s nonparametric regression function estimates have significantly smaller sample mean integrated square error than that of the LLE’s. And the latter method’s coefficient estimates of parametric regression component have significantly smaller mean square errors than that of the former’s.
