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Predictive Inference for the Elliptical Linear Model

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  • Kibria, B. M. Golam
  • Haq, M. Safiul

Abstract

This paper derives the prediction distribution of future responses from the linear model with errors having an elliptical distribution with known covariance parameters. For unknown covariance parameters, the marginal likelihood function of the parameters has been obtained and the prediction distribution has been modified by replacing the covariance parameters by their estimates obtained from the marginal likelihood function. It is observed that the prediction distribution with elliptical error has a multivariate Student'st-distribution with appropriate degrees of freedom. The results for some special cases such as the Intra-class correlation model, AR(1), MA(1), and ARMA(1,1) models have been obtained from the general results. As an application, the[beta]-expectation tolerance region has been constructed. An example has been added.

Suggested Citation

  • Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:235-249
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    References listed on IDEAS

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    1. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    2. Chib, Siddhartha & Tiwari, Ram C. & Jammalamadaka, S. Rao, 1988. "Bayes prediction in regressions with elliptical errors," Journal of Econometrics, Elsevier, vol. 38(3), pages 349-360, July.
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    Cited by:

    1. Dong, Xiaoyu & Mathew, Thomas, 2015. "Central tolerance regions and reference regions for multivariate normal populations," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 50-60.
    2. Wagner J. F. Silva & Renata M. C. R. Souza & F. J. A. Cysneiros, 2022. "Bivariate elliptical regression for modeling interval-valued data," Computational Statistics, Springer, vol. 37(4), pages 2003-2028, September.
    3. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    4. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "A note on Bayesian spatial prediction using the elliptical distribution," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 271-276, September.
    5. 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.
    6. Anwar Joarder, 2008. "Some useful integrals and their applications in correlation analysis," Statistical Papers, Springer, vol. 49(2), pages 211-224, April.

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