New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study

Vassilly Voinov; Natalie Pya; Rashid Makarov; Yevgeniy Voinov

doi:10.1080/03610926.2014.901370

New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study

Vassilly Voinov, Natalie Pya, Rashid Makarov, Yevgeniy Voinov

Research output: Contribution to journal › Review article

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3249-3263
Number of pages	15
Journal	Communications in Statistics - Theory and Methods
Volume	45
Issue number	11
DOIs	https://doi.org/10.1080/03610926.2014.901370
Publication status	Published - Jun 2 2016

Keywords

Chi-squared goodness-of-fit tests
Invariant and consistent tests
Multivariate normality
Power of tests
Symmetric alternatives

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610926.2014.901370

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Cite this

Voinov, V., Pya, N., Makarov, R., & Voinov, Y. (2016). New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study. Communications in Statistics - Theory and Methods, 45(11), 3249-3263. https://doi.org/10.1080/03610926.2014.901370

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