Characterizations of multivariate normality. I. Through independence of some statistics

C. G. Khatri and C. Radhakrishna Rao

Journal of Multivariate Analysis, 1976, vol. 6, issue 1, 81-94

Abstract: It is established that a vector variable (X1, ..., Xk) has a multivariate normal distribution if for each Xi the regression on the rest is linear and the conditional distribution about the regression does not depend on the rest of the variables, provided the regression coefficients satisfy some mild conditions. The result is extended to the case where Xi themselves are vector variables.

Keywords: Multivariate; normal; distribution; characterization; of; multivariate; normality; multiple; regression; and; independence (search for similar items in EconPapers)
Date: 1976
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