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 journalReview articlepeer-review

    10 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 languageEnglish
    Pages (from-to)3249-3263
    Number of pages15
    JournalCommunications in Statistics - Theory and Methods
    Volume45
    Issue number11
    DOIs
    Publication statusPublished - 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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