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題 名 | 從降低預測風險函數來決定最佳預測變數組合=Determination of the Optimal Subsets of Predictor Variables by Minimizing the Prediction Risk Function |
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作 者 | 郭寶錚; 林永立; 何兆銓; | 書刊名 | 農林學報 |
卷 期 | 48:1 1999.03[民88.03] |
頁 次 | 頁61-71 |
分類號 | 319.51 |
關鍵詞 | 所有可能的回歸; 風險函數; 預測風險函數; 交叉確認; 廣義交叉確認; All-possible-regression; Risk function; Prediction risk function; Cross-validation; CV; Generalized cross-validation; GCV; |
語 文 | 中文(Chinese) |
中文摘要 | 回歸模式建構的目的之一,在於藉由觀測得的預測變數與反應變數建立一個對未 來具有預測能力的回歸方程式。在建構的過程中,常需由一群潛在的預測變數中,找出一些 最佳預測變數的組合,以做為決定最後採用模式的基礎,因此有不同的準則可供決定那個預 測變數組合最佳。 在所有可能的回歸搜尋法( all-possible-regression )中,常見的準 則有 R �插AMSE 及 PRESS 等。本文擬從降低預測風險函數的觀點,利用預測風險函數的估 式:□,CV 及 GCV 來做為決定最佳預測變數組合的準則,並將舉例說明從降低預測風險函 數的準則與一般常見的準則所得到的結果一致, 但 GV 及 GCV 準則中無需估計變方(σ�� ),因此在σ�揖憚儔庰L法找到適當估式下,不失為一有效的方法。 |
英文摘要 | One of the purposes of regression analysis is to build a model between predictor and response variables, which may be used for prediction of future observations. In the model-building step, all of the potential predictor variables are examined to select a few "optimal" subsets of predictor variables. These few subsets are candidates for building the final model. Some criteria such as R��, MSE, and PRESS were employed to decide which combinations of predictor variables were optimal in all-possible-regression search. In this study, we tried to find the optimal subsets of predictor variables by minimzing the prediction risk function. It was found that the proposed criteria CV or GCV could get the same subsets of predictor variable as the other criteria. When σ �惺s unknown or no proper estimate exists, the CV or GCV criteria could provide useful information. |
本系統中英文摘要資訊取自各篇刊載內容。