Characterizations of multivariate normality II. Through linear regressions

C. G. Khatri

Journal of Multivariate Analysis, 1979, vol. 9, issue 4, 589-598

Abstract: It is established that a vector (X'1, X'2, ..., X'k) has a multivariate normal distribution if (i) for each Xi the regression on the rest is linear, (ii) the conditional distribution of X1 about the regression does not depend on the rest of the variables, and (iii) the conditional distribution of X2 about the regression does not depend on the rest of the variables, provided that the regression coefficients satisfy some more conditions that those given by [4]J. Multivar. Anal. 6 81-94].

Keywords: Matrices; rank; of; a; matrix; g-inverse; multivariate; normality; multiple; linear; regression; degenerate; distribution; nonsingular; distribution (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (7)

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