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

By

  TAKEAKI KARIYA, Hitotsubashi University

and

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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