مقارنة بعض الاختبارات الحصينة لتحليل التباين المتعدد المتغيراتMANOVA بأستخدام تقديرات- MCD

Abstract

There are many widely used statistics to test the hypothesis of equal means of multivariate populations of a general linear model. One of these is Wilks statistic which is used in this paper. In the case ,when the assumption normality distribution is violated of random error matrix ,then the Wilks statistic leads to a wrong decision. For this reason , Wilks robust statistic ( RFMCD*) has been modified using robust estimations(RFMCD,RMCD,MCD), with changing the cut-off-values. In the case of multi-normal distribution, a cut-off-value is suggested to get a right decision, also cut-off-value is suggested for one and two sided for contaminated multi-normal distribution for the same reason. The method of simulation has been used to generate a random error matrix, that have non– normal distribution, that follow the multi – contaminated normal distribution of one side and the multi – contaminated normal distribution of the two sides. It has been shown, that through using simulation, that the modified robust statistics (RFMCD*) is better than the Classical Wilks statistic presence of outliers from both sides and in some cases, when the outliers are presented in one side, particularly at contamination ratio (є = 0.2 ) , and at any significant level .