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題名 | 區域線性估計量的取樣干擾研究= |
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作者 | 陳萬祥; |
期刊 | 中國統計學報 |
出版日期 | 19920900 |
卷期 | 30:2 1992.09[民81.09] |
頁次 | 頁133-145 |
分類號 | 319.51 |
語文 | chi |
關鍵詞 | 干擾; 取樣; 區域; 線性估計量; |
中文摘要 | 在無母數迴歸分析 (nonparametric regression) 中,等距離固定取樣 (equally spaced fixed design) 是一種常用的取樣方式。但實務上,有時受到若干因素影響,實際的取樣點 (design point) 與事先選定的等距離分布取樣點之間,會產生些微隨機差異 (random variation)。在此情況下,本文得出兩個迴歸函數估計量(estimator) 的漸近均方差 (asymptotic mean square error)。這兩個估計量是Fan (1991) 的區域線性估計量 (local linear smoother) 與Gasser和Mueller (1979) 的核估計量(kernel estimator)。由此結果得知,前者漸近均方差不會受到取樣點的些微隨機變化影響,反之,後者卻會受到影響。另外,當取樣點具有較大程度的隨機變化時,本文也給出前者的漸近均方差。由此結果,我們可了解前者的漸近均方差收斂到零的速度,是如何隨取樣點的隨機建化程度增大而降低。 |
英文摘要 | For nonparametric regression, the equally spaced fixed design is considered in practice very often. However, due to some unknown factors, there might be a slight random variation (RV) between the design points applied and these determined in advance. In this case, we study asymptotic mean square errors (AMSE)of two regression function estimators, the local linear smoother given in Fan (1991 )and the kernel estimator proposed by Gasser and Muel1er (1979).By these AMSE, asymptotic behaviors of the former are not affected by the slight RV, but those of the latter are. We also give the AMSE of the former in other cases of the magnitude of the RV. This result shows clearly how its asymptotic behaviors are affected by the magnitude of RV. |
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