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Characterizations of multivariate normality II. Through linear regressions

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  • Khatri, C. G.

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].

Suggested Citation

  • Khatri, C. G., 1979. "Characterizations of multivariate normality II. Through linear regressions," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 589-598, December.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:4:p:589-598
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    Citations

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    Cited by:

    1. Díaz-García, José A. & González-Farías, Graciela, 2005. "Singular random matrix decompositions: Jacobians," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 296-312, April.
    2. Chen, Pinyuen & Melvin, William L. & Wicks, Michael C., 1999. "Screening among Multivariate Normal Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 10-29, April.
    3. Srivastava, Muni S. & von Rosen, Dietrich, 1998. "Outliers in Multivariate Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 195-208, May.
    4. Díaz-García, José A. & Jáimez, Ramón Gutierrez & Mardia, Kanti V., 1997. "Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 73-87, October.
    5. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    6. Mukhopadhyay, N., 1999. "Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 250-263, February.
    7. Nagao, Hisao & Srivastava, M. S., 2002. "Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 259-273, May.

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