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標題: I 準則之極大極小化裂區設計
minimax criterion for I-optimal split-plot designs
作者: 陳昱霖
Yu-Lin Chen
關鍵字: 穩建設計;I 準則影響值;損失函數;座標轉換;均方誤差;比較預測變異數;Robust design;I-efficiency;Coordinate-exchange;Loss function;Mean squared error;Relative prediction variance
我們想要建立一個模型,能使一裂區設計最佳化。許多準則方法只注重在最佳化變異數參數估計,而忽略偏誤的部分。例如:D 準則最佳設計、A 準則最佳設計與I 準則最佳設計,然而,因子設計通常是複雜的,在模型假設下容易發生錯誤,若有重要的作用項沒有放在模型裡,則會有較大的偏誤。所以,一個好的裂區設計,是要掌控好參數估計中偏誤與變異數。我們建立均方誤差(MSE) 與損失函數(Loss function),藉由損失函數來判斷裂區設計優劣。此論文使用I 準則,利用預測變異數,建立好損失函數,來比較兩設計。

In this paper, we construct split-plot designs that are robust under model misspecification. Many criteria such as the D- criterion, A-criterion and I-criterion only
focus on minimizing the variance of the parameter estimation while ignoring the bias. However, the fitted model is often misspecified. If there exist significant effects that are not in the model, the bias will be large. Therefore, a good split plot design should control the variance and bias of the estimates. We establish the mean square error (MSE) and loss function. We use the loss function to determine good designs.
Rights: 同意授權瀏覽/列印電子全文服務,2017-07-19起公開。
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