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題 名 | 區域線性估計量的權數簡化研究 |
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作 者 | 朱至剛; | 書刊名 | 中國統計學報 |
卷 期 | 30:1 1992.03[民81.03] |
頁 次 | 頁77-86 |
分類號 | 319.51 |
關鍵詞 | 估計量; 區域線性; 權數; |
語 文 | 中文(Chinese) |
中文摘要 | 在固定設計 (fixed design) 以及隨機設計(random design) 的兩種無母數回歸分析模型中,Mueller (1987) 與Fan (1991) 分別證明了區域線性估計量 (local linear smoother) 具有良好的迴歸函數估計結果。本文發現,在構造區域線性估計量時,欲達到此良好的迴歸函數估計效果,我們可以用一個較低階的多項式,其階數 (order) 比Mueller (1987) 與 Fan (1991) 所使用的多項式之階數要低,來局部逼近 (local approximation) 迴歸函數。對此,我們可以降低構造此估計量所需要的計算量。更進一步,我們可以運用非負值的權數函數,以避免使用Mueller (1987)的具有負值的權數函數。如此,在解釋區域線性估計量的結構時比較自然,易懂。最後按照本文建議方法所構造出來的區域線性估計量,其漸近變異數(asymptotic variance)與漸次偏差量(asymptotic bias) 均與Mueller (1987)和Fan (1991)所獲得的結果相同。 |
英文摘要 | In the cases of the fixed design and the random design nonparanetric regression, Mueller (1987)阻d Fan (1991) have shown that the local linear smoother (LLS) has. good performance in the estimation .of a regression function. In this paper, the construction of the LLS is simplified by the following approaches. In the sense of the asymptotic variance and the asymptotic bias, the simplified LLS has the sane performance as the ordinary LLS. To construct the simplified LLS, we first use a polynomia1 of smaller order than that applied in Mueller (1987) and Fan (1991) to approximate the regression function locally. In this case, the amount of calculation required in the construction of the LLS can be reduced. Second, we use a nonnegative weight function to construct the local weights. The weight function which has negative va1ues at some points applied in Mueller (1987) can be left out in the construction of the LLS, In this case, the idea of the estimator constructed can be understood easily. |
本系統中英文摘要資訊取自各篇刊載內容。