高維度下複合式T2檢定

The Decomposite T2 -Test Under Large Dimension

蔡嘉軒(Chia-Hsuan Tsai)

指導教授 ： 陳志榮 ； 洪慧念

國立交通大學/理學院/統計學研究所/博士(2020年)

摘要

在此篇文章中，將 Ledoit and Wolf 所提出在旋轉不變性下得到的最佳共變異數反矩陣估計值，在高維度設定下，處理假設檢定問題。當資料維度很大時，吾人稱此檢定統計量類型為複合式T檢定統計量。一併將探討此檢定統計量在有範圍限制下的對立假設下，其近似分配以及近似檢定力。由模擬結果、與過往文獻中提到的近似檢定力函數做比較，以及將此檢定統計量套用於實際臺北捷運資料，做不同重抽方法下的無母數檢定分析，可以看到使用此檢定統計量能得到較佳檢定力的優點。

關鍵字

複合式 T 檢定 ； 高維度下共變異數矩陣 ； 旋轉不變性估計值

並列摘要

In this paper, an asymptotically optimal rotation-equivariant estimator of the inverse
of the population covariance from decision theoretical point of view proposed by Ledoit and Wolf is incorporated to construct the T^2 type test statistics. When the dimension is large, we call such T^2 type test statistics the decomposite T^2-test in this paper. The asymptotic distribution of the proposed test statistic under sequence of local alternatives is studied. Simulation studies and a real data analysis are presented to show the merits of the proposed test statistic.

並列關鍵字

Decomposite T test ； high-dimensional covariance matrix ； rotation-equivariant estimator

參考文獻

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