A powerful affine invariant test for multivariate normality based on interpoint distances of principal components. Issue 5 (28th May 2018)

• Record Type: Journal Article
• Authors: Madukaife, Mbanefo S.; Okafor, Fabian C.
• Is Part Of: Communications in statistics. Volume 47:Issue 5(2018)
• Page Start: 1264
• Page End: 1275
• Publication Date: 2018-05-28
• Subjects: Empirical power -- Multivariate normality -- Principal components -- Population pth quantile -- Q-Q plot -- Type-I error rate; 62E10 -- 62E20 -- 62H05; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1309667
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: In this paper, a probability plots class of tests for multivariate normality is introduced. Based on independent standardized principal components of a d-variate normal data set, we obtained the sum of squared differences between corresponding observations of an ordered set of each principal component observations and the set of the population p th quantiles of the standard normal distribution. We proposed the sum of these d-sums of squared differences as an appropriate statistic for testing multivariate normality. We evaluated empirical critical values of the statistic and compared its power with those of some highly regarded techniques with a wonderful result.