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題名 | 脊迴歸模型中不同估計方法之比較=Comparison of Different Estimation Methods in Ridge Regression Models |
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作者 | 蔡宗儒; 吳美儒; Tsai, Tzong-ru; Wu, Mei-ju; |
期刊 | 中國統計學報 |
出版日期 | 20010300 |
卷期 | 39:1 2001.03[民90.03] |
頁次 | 頁73-94 |
分類號 | 319.22 |
語文 | chi |
關鍵詞 | 共線性; 脊迴歸分析法; 模糊加權; 離群值; Fuzzy-weighted method; Multicollinearly; Outliers; Ridge regression; |
中文摘要 | 為解決迴歸模型中解釋變數所產生的共線性問題,Hoerl 及Kennard (1970) 提出了脊迴歸分析法。根據脊迴歸分析法 所得到的迴歸參數估計量之總變異會較最小平方估計量的總變異穩定。但傳統的脊迴歸字數估計量並非一個不偏的估計量,於是謝邦昌及周玫芳 (1998) 建議將摺刀法應用於傳統脊迴歸分析中來減低脊迴歸參數估計量所造成的偏誤,此法稱改良式脊迴歸分析法。然而,改良式脊迴歸分析;去並沒有考慮資料含有離群值的情形。假定資料中含有離群值,則整個脊迴歸參數估計問題將會變得更加的複雄。Tsat(1999) 建議在原始的脊迴歸估計中加入模糊權數而形成模糊脊迴歸估計法。此法結合模糊加權估計及脊迴歸估計的優點,使得離群值在迴歸參數估計中的影響可以減到最低。本文旨在比較當資料含有離群值時的各種不同的參數估計方法在估計上的穩定性。這些方法包括了最小平方法、模糊加權估計法、脊迴歸分析法、改良式脊迫歸分析:去及模糊加權脊迴歸估計法。 |
英文摘要 | It is well known that the ridge regression method suggested by Hoerl and Kennard (1970) to deal with the multicollinearity problem of regression models is biased although its variance is more stable than that of least squares estimator. Shia and Chow (1998) suggested an improved ridge regression method by combining the jackknife method and ridge regression estimation method. According to the simulations of Shia and Chow (1998), the improved ridge regression estimator can reduce the bias in ridge regression estimation. The improved ridge regression estimation, however, does not consider the presence of the outliers. Tsai (1999) suggested to add fuzzy weights into the ridge regression estimation and proposed a fuzzy-weighted ridge regression estimation method which effectively reduces the influence of outliers. In this paper, different estimation methods are compared in ridge regression model. These estimation methods contain ordinary least square method, fuzzy-weighted estimation method, ridge regression method, improved ridge regression analysis method and fuzzy-weighted ridge regression estimation method. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。