การเปรียบเทียบประสิทธิภาพตัวสถิติทดสอบสำหรับการแจกแจงปรกติหลายตัวแปร
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Abstract
Abstract
The objective of this research is to compare the efficiency of four statistical tests–Mardia’s, Mardia and Kent’s, Koizumi et al.’s and Hanusz and Tarasinska’s statistical tests–for multivariate normal distribution. Three variables (p) and three levels of covariance matrix for multivariate distribution are defined. The sample size (n) for this study equals 20, 30, 50, 70, 100, 150 and 200. The simulation data are conducted 126 situations by Monte Carlo technique and replicated 2,000 times for each situation. The criterion for efficiency comparison is power of the test which the statistical tests can only control type I error. The conclusions of this research are as follows: Mardia’s statistical test and Mardia and Kent’s statistical test tend to control the probability of type I error at the significant level 5 % for a large sample size. However, Koizumi et al.’s statistical test and Hanusz and Tarasinska’s statistical test tend to control the probability of type I error for all situations. When considering power of the test, it is found that Koizumi et al.’s statistical test tends to have the highest power of the test for multivariate t distribution with 2 and 4 degrees of freedom, multivariate lognormal and multivariate cauchy distributions for all situations.
Keywords: statistical test; multivariate normal distribution; type I error; power of the test
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