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New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study
Authors:Vassilly Voinov  Natalie Pya  Rashid Makarov  Yevgeniy Voinov
Affiliation:1. KIMEP University, Almaty, Kazakhstan;2. Institute for Mathematics and Mathematical Modeling, Almaty, Kazakhstanvoinovv@mail.ru;4. Institute for Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Abstract:
ABSTRACT

New invariant and consistent goodness-of-fit tests for multivariate normality are introduced. Tests are based on the Karhunen–Loève transformation of a multidimensional sample from a population. A comparison of simulated powers of tests and other well-known tests with respect to some alternatives is given. The simulation study demonstrates that power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests. However, averaged over all of the simulated conditions examined in this article, the Anderson–Darling type and the Cramer–von Mises type tests seem to be the best.
Keywords:Chi-squared goodness-of-fit tests  Invariant and consistent tests  Multivariate normality  Symmetric alternatives  Power of tests.
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