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題 名 | 區域脊迴歸估計量的漸近性質研究(2)=Asymptotic Properties of the Local Ridge Regression Estimator (Ⅱ) |
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作 者 | 林宏宗; | 書刊名 | 中國統計學報 |
卷 期 | 36:1 1998.03[民87.03] |
頁 次 | 頁43-53 |
分類號 | 319.51 |
關鍵詞 | 區域線性估計量; 區域脊迴歸估計量; 無母數迴歸; 隨機取樣; 脊迴歸; 邊界效應; Local linear smoother; Local ridge regession estimator; Nonparametric regression; Random sampling; Ridge regession; Boundary effects; |
語 文 | 中文(Chinese) |
中文摘要 | 在隨機取樣(random design)的無母數迴歸分析(nonparametric regression)中, 為了避開Fan(1993)的區域線性估計量(local linear smoother)會產生無限大的條件變異 數(conditional variance)的缺點,Seifert和Gasser(1996)提議將脊迴歸(ridge regression) 應用到區域線性估計量。本文稱如此所得到的估計量為區域脊迴歸估計量(local ridge regression estimator)。然而Seifert和Gasser(1996)並沒有說明區域脊迴歸估計量的理論性 質。Deng(1998)則研究了這個估計量在估計迴歸函數(regression function)本身時的漸近 性質。本文目的則在研究此估計量在迴歸函數具有多階導數的情況之下,估計迴歸函數及其 各階導數(derivatives)的漸近性質。我們發現,在此情況之下,不管脊迴歸參數如何選取, 在取樣點發生區域內部(interior),區域脊迴歸估計量會較Fan(1993)的區域線性估計量 有較慢的收斂速度。另一方面,若在取樣點發生區域的邊界(boundary regions),則區域脊 迴歸估計量會有邊界效應(boundary effects)的麻煩。 |
英文摘要 | In the case of the random design nonparametric regression, to correct for the infinite conditional variance of the local linear smoother in Fan (1993), Seifert and Gasser (1996) propose to apply the idea of ridge regression to the local linear smoother. The resulting estimator is called the local ridge regression estimator in this paper. However, the asymptotic properties of the new estimator are not addressed by Seifert and Gasser (1996). They are studied by Deng (1998) when estimating the regression function itself, under the assumption that the regression function has two derivatives. In this paper, we shall study its asymptotic properties when estimating the regression function and its derivatives. We found that, in the case that the regression functioin has more derivatives. on matter how the ridge regression parameters are selected, the asymptotic performance of the resulting local ridge regression estimator will be inferior to that of the local linear smoother. |
本系統中英文摘要資訊取自各篇刊載內容。