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Predictive inference for singular multivariate elliptically contoured distributions

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  • Liu, Jin Shan
  • Ip, Wai Cheung
  • Wong, Heung

Abstract

We have derived the predictive distributions of future responses and the regression matrix in the multivariate linear regression model, under the singular or nonsingular matrix variate elliptically contoured distribution with noninformative prior, with respect to the Hausdorff measure. The predictive distributions are also derived under the singular or nonsingular matrix variate normal distribution with normal-inverse Wishart conjugate prior as a particular case of the matrix elliptically contoured distribution. The predictive distributions are singular or nonsingular matrix-T distributions introduced by Diaz-Garcia and Gutierrez-Jaimez [J.A. Diaz-Garcia, R. Gutierrez-Jaimez, Distribution of the generalized inverse of a random matrix and its applications, J. Statist. Plann. Inference 136 (2006) 183-192], both in the noninformative and conjugate prior cases. The first result gives inference robustness with respect to departures from the underlying distribution assumption in the direction of elliptically contoured distributions, even in the singularly distributed case.

Suggested Citation

  • Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1440-1446
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    References listed on IDEAS

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    1. Nkurunziza, Sévérien & Chen, Fuqi, 2013. "On extension of some identities for the bias and risk functions in elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 190-201.

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