A shrinkage robust ridge estimator with an intercept term

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林庭羽(Ting-yu Lin) 查詢紙本館藏

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論文名稱

(A shrinkage robust ridge estimator with an intercept term)

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摘要(中)

如果數據包含異常值與多重共線性時，則通常相較於最小平⽅法會選用 Ridge M-estimator(Silvapulle 1991)。因為當數據同時具有異常值與多重共線性的情況下，Ridge M-estimator 會有較小的MSE。許多的估計量，例如：Pretest M-estimators, Stein-type shrinkage M-estimators，都類似Ridge M-estimator。然⽽現在所有的ridge estimators 和M-estimators 都沒有考慮截距項的收縮估計。因此存在改進現有估計量的空間，可透過改進截距項的估計⽽達成。在本⽂中，我們透過引⼊截距項的估計⽅法，在線性模型中引⼊新的 robust estimators 的估計。為了說明，我們分析了從數據提取系統（KGUSBADES）提供的Nikkei NEEDS 公司財務數據。本論⽂是與Kwansei Gakuin ⼤學的Jimichi Masayuki 博⼠及其同事合作的⼀部分。但是，所有統計分析都是由作者進⾏的。

摘要(英)

If the data contains outliers and multicollinearity, the ridge M-estimator (Silvapulle 1991) is the preferred estimator to the usual least square estimator. In fact, the ridge M-estimator has the smaller mean square error in the presence of outliners and multicollinearity. Many other estimators, such as the pretest M-estimators and Stein-type shrinkage M-estimators follow similar approaches to the ridge M-estimator. However, all the existing ridge and M-estimators do not consider shrinkage
estimation for the intercept term. Hence, there is a room for improving the existing estimators by improving the estimator of the intercept. In this thesis, we introduce new robust estimators of regression coefficients in a linear model by introducing a pretest estimation method for an intercept. For illustration, we analyze the Nikkei NEEDS corporate finance data that are provided from the
data-extraction system (KGUSBADES). This thesis is part of collaboration with Dr. Jimichi Masayuki and his
olleagues in Kwansei Gakuin University. However, all the statistical analyses are conducted by the author.

關鍵字(中)

★ 異常值
★ 多重共線性
★ 影響函數
★ 脊迴歸

關鍵字(英)

★ Influence function
★ Multicollinearity
★ Outlier
★ Robust estimator
★ Ridge estimator

論文目次

1. Introduction ……………………………………………...………………………....4
2. Background …………………………………………………………...……………………….5
3. Proposed Method ………………………………………………………………………… 16
4. Simulation …………………………………………………………………………….....18
5. Data analysis ……………………………………………………………...….…….24
6. Conclusion …………………………………………………………………...…………..29
7. Appendix …………………………………………………………………...…………....30
8. References …………………………………………………………………...…………..33

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指導教授

江村剛志(Takeshi Emura)

審核日期

2019-8-22

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