- 期刊
多變量常態的多重檢定實證研究
The Empirical Study of Multiple Test Procedures for Assessing Multivariate Normality
摘要
由於多變量常態檢定並不存在一個具全方位檢定力（uniformly powerful）的統計量，因此當各種具檢定力的檢定方法做出不同判決時，不知道該相信哪一個？Tenreiro（2011）根據Fromont and Laurent（2006）所提出改良型的 Bonferroni校正法，建立一套檢定多變量常態的多重檢定程序。該程序包含了四個在面對不同特性的對立假說時，各具高檢定力的統計量，試圖藉群組力量，截長補短，使之具備全方位檢定力。而其蒙地卡羅實驗也驗證了這個想法。本文藉由這個多重比較的概念，並根據Bonferroni校正法的原理，認為較少數量的組合應該能提供較高檢定力，只要組成群組的統計量也具備對廣泛的對立假說的檢定力。由於本文作者曾提出一個深具競爭力的統計量W_(min,m)（5）（Wang and Hwang, 2011），認為可以取代Tenreiro（2011）的四個組合成員之兩個或甚至三個，成為新的多重檢定的組合。透過與 Tenreiro（2011）同樣的實證研究，發現新的組合中，以三個成員組合的多重檢定表最好，不但整體表現優於Tenreiro（2011）的四個統計量的組合，也同樣展現全方位的檢定力。
並列摘要
This paper proposes two multiple test procedures for assessing multivariate normality, and compares the test power with the one proposed by the original author Tenreiro (2011) by means of Monte Carlo simulation. The idea of using a multiple test procedure comes from the fact that there is no uniformly powerful statistic, so when various testing methods make different decisions, which one to believe? Tenreiro (2011) established a multiple test procedure based on the modified Bonferroni correction method proposed by Fromont and Laurent (2006). The procedure contains four statistics each showing high power in facing alternative distributions of various shapes. And its Monte Carlo experiment also verified that this procedure showed overall good performance. Using this concept of multiple tests, and based on the principle of the Bonferroni correction method, this paper argues that a smaller number of multiple tests should provide higher test power, as long as the statistics that make up the group also have test power against a wide range of alternative hypotheses. Since the author of this paper have proposed a highly competitive statistic W_(min,m)(5) (Wang and Hwang, 2011) that can replace two or even three of the four combinatorial members of Tenreiro (2011), two new combinations of the multiple test procedure are then checked. Through the same empirical research as Tenreiro (2011), it is found that among the new combinations, the multiple test procedure with three statistics outperforms the combination of the four statistics of Tenreiro (2011).