Autore: Najarzadeh, Dariush
Titolo: Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions
Periodico: Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2019 - Volume: 28 - Fascicolo: 4 - Pagina iniziale: 593 - Pagina finale: 623

For ap-variate normal distribution with covariance matrix, the standardized gener-alized variance (SGV) is defined as the positivepth root of||and used as a measureof variability. Testing equality of the SGVs, for comparing the variability of multi-variate normal distributions with different dimensions, is still regarded as matter ofinterest. The most classical test for this problem is the likelihood ratio test (LRT).In this article, testing equality of the SGVs ofkmultivariate normal distributionswith possibly unequal dimensions is studied. To test this hypothesis, two approxi-mations for the null distribution of the LRT statistic are proposed based on the wellknown Welch–Satterthwaite and Bartlett adjustment distribution approximation meth-ods. Furthermore, the high-dimensional behavior of these approximated distributionsis also investigated. Through a wide simulation study: first, the performance of theproposed tests with the classical LRT is compared in terms of type I error, power, andalpha adjusted equivalents; second, the robustness of the procedures with respect todepartures from normality assumption is evaluated. Finally, the proposed methods areillustrated with two real data examples.




SICI: 1618-2510(2019)28:4<593:TEOSGV>2.0.ZU;2-6

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