高維兩常態母體平均向量之檢定

A two-sample test for high-dimensional normal mean vector

楊博舜(Po-Shun Yang)

指導教授 ： 周若珍

國立清華大學/理學院/統計學研究所/碩士(2014年)

摘要

當資料維度相較於樣本數為大時，傳統在多維使用的檢定方法將不再適用，近期的研究也提出一些在高維的檢定方法。本文提出一平均向量檢定適用於高維兩獨立常態母體，並試圖推導其漸進檢定力函數，藉由模擬實驗可以比較該檢定與近期方法在虛無及對立假設為真下之表現，最後以柏拉圖著作集和大腸癌DNA微陣列兩資料為範例，作該檢定能否區別兩母體平均向量之實例分析。

關鍵字

常態分配 ； 兩母體檢定 ； Behrens-Fisher 問題 ； 高維度資料

並列摘要

When the data dimension is large relative to the sample size, some of the conventional multivariate testing procedures cannot be applied. Recent studies have proposed some test statistics applicable to high-dimensional data. In this thesis, a new test for testing the equality of the mean vectors of two independent normal distributed populations is proposed. Furthermore, the asymptotic power function is obtained. Some simulations are carried out to compare its performance with some existing tests under null and alternative hypotheses, respectively. Finally, the test is applied to Plato's works data and DNA microarray gene expression data of colon cancer tissues to see if it can distinguish the difference between two population mean vectors.

並列關鍵字

normal distribution ； Two-sample test ； Behrens-Fisher problem ； High-dimensional data

參考文獻

呂政勳 (2011), “高維 Behrens-Fisher 問題”, 碩士論文, 國立清華大學。

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