Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 3, pp. 440--451
LBI TESTS FOR MULTIVARIATE NORMALITY IN CURVED FAMILIES AND MARDIA'S TEST
TAKEAKI KARIYA, Hitotsubashi University
EDWARD I. GEORGE, University of Texus at Austin
SUMMARY. Generalizing the arguments in Kuwana and Kariya (1991), the general form of a LBI (local best invariant) test is obtained for testing multivariate normality in a curved family. It is also shown that Mardia's kurtosis test is LBI against a new family of multivariate alternatives. General rules for asymptotic null and nonnull distributions of a LBI test statistic are obtained. A measure of local departure of a curved family from normality is defined.
AMS (1980) subject classification. Primary 62H15, secondary 62H10.
Key words and phrases. locally best invariant test, Mardia's kurtosis test, multivariate mixture, multivariate normality.
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