A test for multivariate normality based on sample entropy and projection pursuit

Abstract

Testing normality and multinormality has long been an interesting issue in statistical inferences. Many tests have been proposed. In particular, Vasicek ( J. Roy. Statist. Soc. A 139 (1976), 54–59) suggested a test based on sample entropy. A similar idea was extended to the multivariate case with projection pursuit for searching for departure from the multivariate normal distribution. We, in this paper, suggest a new test for multinormality based on density estimation, a number-theoretic method, projection pursuit technique and sample entropy. Our results show that the new test may be recommended for practice.