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Multivariate normality via conditional specification |
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| Authors: | Barry C. Arnold, Enrique Castillo,Jos Marí a Sarabia |
| Affiliation: | a Department of Statistics, University of California, Riverside, CA 92521-0318, USA b Universidad de Cantabria, Santander, Spain |
| Abstract: | If X is a k-dimensional random vector, we denote by X(i) the vector X with coordinate i deleted and by X(i,j) the vector X with coordinates i and j deleted. If for each i the conditional distribution of Xi given X(i) = x(i) is univariate normal for each x(i) K−1 and if for each i, j the conditional distribution of Xi given X(i,j) = x(i,j) is univariate normal for each x(i,j) k−2 then it is shown that X has a classical k-variate normal distribution. |
| Keywords: | Normal conditionals Classical normal distribution Conditional specification |
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