A new large sample goodness of fit test for multivariate normality based on chi squared probability plots

ABSTRACT

Based on a chi square transform of the multivariate normal data set, we proposed a technique for testing multinormality which is the sum of interpoint squared distances between an ordered set of the transformed observations and the set of the population pth quantiles of the chi squared distribution. The critical values of the test were evaluated for different sample sizes and random vector dimensions through extensive simulations. The empirical type-I-error rates and powers of the proposed test were compared with those of some other well known tests for MVN with the proposed test showing excellent results at large sample sizes.

KEYWORDS:

• Multivariate normality
• Interpoint distance
• kth order statistic
• Empirical power
• type-I error rate

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E10
• 62E20