A class of Liu-type estimators based on ridge regression under multicollinearity with an application to mixture experiments

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陳愛群(Ai-Chun Chen) 查詢紙本館藏

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論文名稱

(A class of Liu-type estimators based on ridge regression under multicollinearity with an application to mixture experiments)

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摘要(中)

線性回歸中，在共線性問題發生的情況下，常見的最小平方估計量表現得並不理想。這類問題發生在混合實驗 ( mixture experiments ) 中，原因是此種實驗對自變數 ( regressors ) 的數學限制式所導致的。Hoerl和Kennard在1970年提出了ridge 回歸方法的概念，解決了最小平方估計量在共線性問題下的缺陷。近來，ridge回歸方法也成功地應用在混合實驗中。然而，混合實驗通常會將截距項合併至自變數的係數之中，若我們在線性模型中保有截距項並對自變數做標準化的話，ridge回歸方法的應用將變得比較複雜。此篇論文考慮了一種特殊的劉氏估計量( Liu-type estimators )，並保有模型中的截距項。我們推導新估計量的均方差( mean squared error )函式並且透過統計模擬來比較新估計量和既有的ridge估計量。最後，我們用兩組實驗的資料來說明新估計量的表現。

摘要(英)

In the linear regression, the least square estimator does not perform well in terms of mean squared error when multicollinearity exists. The problem of multicollinearity occurs in industrial mixture experiments, where regressors are constrained.Hoerl and Kennard (1970) proposed the ordinary ridge estimator to overcome the problem of the least squared estimator under multicollinearity. Recently, the ridge regression is successfully applied to mixture experiments. However, the application of ridge becomes difficult if the linear model has the intercept term and the regressors are standardized as occurring in mixture experiments. This paper considers a special class of Liu-type estimators (Liu, 2003) with intercept. We derive the theoretical formula of the mean squared error for the proposed method. We perform simulations to compare the proposed estimator with the ridge estimator in terms of mean squared error. We demonstrate this special class using the dataset on Portland cement with mixture experiment (Woods et al., 1932).

關鍵字(中)

★ 均方差
★ 共線性
★ Ridge回歸方法
★ Shrinkage估計量

關鍵字(英)

★ Mean squared error
★ Multicollinearity
★ Ridge regression
★ Shrinkage estimator

論文目次

摘要 …….………………………………………………………………………………………...I

Abstract ...………………………………………………………………………………………..II

致謝辭 ...…………………………………………………………………………………………III

Contents ...………………………………………………………………………………………IV

List of Tables …………………………………………………………………………………….V

List of Figures …………………………………………………………………………………..VI

1. Introduction ………………………………………………………...………………………....1

2. Background …………………………………………………………...……………………….2

3. Proposed Method ……………………………………………………………………............ 10

4. Theory………………………………………………………………..……………….……….14

5. Simulation ………………………………………………………………………...…………..22

6. Data analysis ………………………………………………………………………...……….32

7. Conclusion ………………………………………………………………………...………….41

8. Reference ………………………………………………………………………...…………...42

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指導教授

江村剛志(Takeshi Emura)

審核日期

2015-7-30

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