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We consider the problem of testing multivariate normality when the data consist of a random sample of two-step monotone incomplete observations. We define for such data a generalization of Mardia’s statistic for measuring kurtosis, derive the asymptotic non-null distribution of the statistic under certain regularity conditions and against a broad class of alternatives, and provide an application to a well-known data set on cholesterol measurements.

Kurtosis tests for multivariate normality with monotone incomplete data