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題名 | 改良式脊迴歸分析法=Improved Ridge Regression Analysis |
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作者 | 謝邦昌; 周玫芳; Shia, Ben-chang; Chow, May-feng; |
期刊 | 中國統計學報 |
出版日期 | 19980900 |
卷期 | 36:3 1998.09[民87.09] |
頁次 | 頁259-277 |
分類號 | 319.51 |
語文 | chi |
關鍵詞 | 共線性; 脊迴歸分析法; 改良式脊迴歸分析法; 摺刀法估計式; Multicollinearity; Ridge regression analysis; Improved ridge regression analysis; Jackknife estimator; |
中文摘要 | 在應用迴歸分析法時,常會遇到共線性( multicollinearity )的問題,而共線 性的存在會使得最小平方估計式( least square estimator )之總變異( total variance )出現不穩定的情形。針對共線性的問題,Hoerl 及 Kennard ( 1970 )提出脊 迴歸分析法( ridge regression analysis )使其總變異較最小平方估計式穩定, 但傳統 脊迴歸估計式為一個偏量估計式( biased estimator )。 本文應用線性模式之摺刀法( Jackknife ),配合脊迴歸分析法導出改良式脊迴歸估計式,以降低脊迴歸估計式之偏量( bias )。 模擬不同程度的共線性資料之結果顯示,改良式脊迴歸估計式如脊迴歸估計式般 穩定,但對於降低偏量方面有顯著之改善,其預測能力亦優於脊迴歸估計式,因此改良式脊 迴歸估計式較傳統脊迴歸估計式更加穩定且精確,對於迴歸模式而言改良式脊迴歸分析法為 一不錯的方法。 |
英文摘要 | When we use the regression approach, the problem of multicollinearity makes the least squares estimator unstable and interiorates the forecasting ability of the model. Mathematically speaking, the total variance of the resulting estimator would diverge from the normal value considerably. In order to achieve an acceptable level of precision and stability, Hoerl and Kennard ( 1970 ) propose ridge regression analysis which successfully generates a smaller total variance compared favorably to the least squares estimator. However, the estimator employed by conventional ridge regression analysis is a biased estimator, which adversely affects the explanatory ability of the model. In this study, we propose a new approach, called improved ridge regression analysis, by applying the linear Jack-knife to conventional ridge regression analysis. The empirical and simulation results show that the proposed method exhibited a better forecasting feature than the conventional approach both in stability and precision. |
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