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研究生:李沛欣
研究生(外文):Pei-Hsin Lee
論文名稱:具不完整資料的偏斜t因子模型
論文名稱(外文):Skew-t factor analysis models with incomplete data
指導教授:林宗儀林宗儀引用關係
口試委員:吳宏達王婉倫
口試日期:2015-07-22
學位類別:碩士
校院名稱:國立中興大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:43
中文關鍵詞:非對稱性ECM 演算法插補遺失值偏斜t 因子模型受限的 多變量偏斜t 分佈
外文關鍵詞:asymmetryECM algorithmimputationincomplete dataSTFA modelrMST distribution
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  • 點閱點閱:149
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本文中主要著重研究的問題是當連續型多變量資料中包含遺失值時,偏斜t因子(STFA) 模型的最大概似估計。具不完整資料的STFA 模型穩健地延伸古典的因子模型,模型中假設隱藏的因子及不可觀測的誤差項服從受限的多變量偏斜t 分佈,用以因應資料非常態的現象,例如:資料型態具有不對稱、厚尾或是離群值的情形。由於概似函數的處理是很棘手的問題,本篇論文中,我們發展了有利於計算簡化的ECM 演算法,這個方法同時可以計算出最大概似估計值以及針對資料中不完整的部分進行插補值。我們在本文的最後,透過遺失數據的模擬以及兩個真實數據來說明我們所建議的方法相較於現在的方法更為有效。

1 導論1
2 預備知識3
3 具不完整資料的STFA 模型5
3.1 具不完整資料的STFA 模型的性質
3.2 ECM 演算法8
4 計算策略11
4.1 評估ECM-type 演算法的收斂11
4.2 選取模型的準則12
5 真實案例分析13
5.1 鈾礦探勘資料13
5.2 印第安人糖尿病數據資料17
5.3 考古學剝落石片資料20
6 結論26
A. 性質2 的證明27
B. 參數估計值的標準差公式31
C. MGHCStFA 模型34
參考文獻40

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