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http://dx.doi.org/10.5351/CKSS.2005.12.1.071

The Limit Distribution of an Invariant Test Statistic for Multivariate Normality  

Kim Namhyun (Department of Science, Hongik University)
Publication Information
Communications for Statistical Applications and Methods / v.12, no.1, 2005 , pp. 71-86 More about this Journal
Abstract
Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.
Keywords
multivariate normality; goodness-of-fit tests; Gaussian process; Brownian bridge; quantile process;
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Times Cited By KSCI : 1  (Citation Analysis)
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