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研究生:林尚霆
研究生(外文):Lin, Shang-Ting
論文名稱:高維度變異數分析
論文名稱(外文):On High Dimensional Analysis Of Variance
指導教授:周若珍周若珍引用關係
學位類別:碩士
校院名稱:國立清華大學
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:44
中文關鍵詞:變異數分析
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本論文探討當變數個數p大於或等於樣本個數N的高維度情況下變異數分析的問題。討論兩個不同的變異數結構:完全隨機設計與Split-plot設計。本文給出在這兩個情況下的檢定統計量及在虛無及對立假設下的大樣本近似分布。電腦模擬結果給出了該檢定統計量的達成顯著水準與經驗統計力。本文亦將該統計量實際應用在赤箭總體基因體資料的分析,並討論總體基因體資料處理方法的適合性。
In this thesis, MANOVA problem is studied for normal random vectors whose dimension p is larger than or equal to the number of observations N. Two covariance structures are considered, the usual independence design and the split-plot design. Procedures for testing the main effects and the interaction are proposed. Their asymptotic distributions are given under both null and alternative hypotheses. Some simulation results are also provided. Finally, the procedures are applied to metagenomics datasets to study the structure of fungal species in the rhizomes of four Gastrodia species.
1 緒論 1
2 文獻回顧 3
2.1 一維度與多維度兩母體檢定 3
2.2 高維度兩母體檢定 4
3 研究方法與模擬 6
3.1 MANOVA的傳統檢定方法 6
3.2 高維度MANOVA的檢定方法 7
3.3 Split-Plot設計 14
3.4 達成顯著水準與經驗檢定力模擬 18
4 實例研究 23
5 結論 28
參考文獻 29
附錄 32
附錄A 定理1之證明 32
附錄B 附表 36

參考文獻
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