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Characterization of the multivariate normal distribution by conditional normal distributions

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Summary

LetX andY be two random vectors with values in ℝk and ℝ∝, respectively. IfZ=(X T,Y T)T is multivariate normal thenX givenY=y andY givenX=x are (multivariate) normal; the converse is wrong. In this paper simple additional conditions are stated such that the converse is true, too. Furthermore, the case is treated that the random vectorZ=(X T1 , …,X Tt )T is splitted intot≥3 partsX 1, …,X t.

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Authors and Affiliations

  1. Institut für Mathematische Statistik, Universität Karlsruhe, Englerstraße 2, D-7500, Karlsruhe 1, FRG

    W. Bischoff &  W. Fieger

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  1. W. Bischoff
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  2. W. Fieger
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Bischoff, W., Fieger, W. Characterization of the multivariate normal distribution by conditional normal distributions. Metrika 38, 239–248 (1991). https://doi.org/10.1007/BF02613616

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  • DOI: https://doi.org/10.1007/BF02613616

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