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

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