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題 名 | 區域線性估計量的一般性質研究 |
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作 者 | 鄧崇儀; | 書刊名 | 中國統計學報 |
卷 期 | 30:1 1992.03[民81.03] |
頁 次 | 頁63-76 |
分類號 | 319.51 |
關鍵詞 | 估計量; 區域線性; |
語 文 | 中文(Chinese) |
中文摘要 | 在隨機設計 (random design) 的無母數迴歸分析 (nonparametric regression) 中,Fan (1991) 利用區域線性最小平方法 (local linear least squares method) 構造了一個迴歸函數估計量。這個估計量具有優越的漸近變異數 (asymptotic variance)和不錯的漸近偏差量 (asyrmptotic bias) 性質;而且如果我們事前知道隨機設計的密度函數 (design density) 定義域的邊界點,則比估計量沒有邊界效應 (boundary effect)。在本論文中,我們應用Fan的想法來構造迴歸函數各階導數的估計量。我們證明出如果適當的選取區域線性最小平方法中所給定的權數(weight),則得到的迴歸函數導數估計量仍然具有區域線性估計量的上述優點。更進一步地,如果從漸近均方差來看,這些迴歸函數導數計量可且比Gasser-M ueller的迴歸函數導數估計量要來的更好。模擬研究顯示這些漸近性質可以在合理的樣本下表現出來。 |
英文摘要 | For the random design nonparametric regression, Fan (1991) uses the local linear least squares method to construct an estimstor of the regression function. This estimator has advantages of having the superior asymptotic variance quantity and the nice asymptotic bias quality. Also, it does not suffer from boundary effects in the case that boundary points of the support of the design density are known in advance. In this paper, we apply Fan's idea to construct estimators of derivatives of the regression function. It is shown that if the weights given in the local linear least squares are chosen properly, then the resulting estimators of derivatives can be better than those derived from the Gasser-Mueller estimator, in the sence of the asymptotic mean square error. Simulation studies demonstrate that the asymptotic results hold in reasonable sample sizes. |
本系統中英文摘要資訊取自各篇刊載內容。