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  Far East Journal of Theoretical Statistics  
 ISSN: 0972-0863
 
 
 

     Far East Journal of Theoretical Statistics
    Volume 24, Issue 1, Pages 35 - 48 (January 2008)


PREDICTION DISTRIBUTION FOR LINEAR REGRESSION MODEL WITH MULTIVARIATE STUDENT-t ERRORS

Azizur Rahman (Australia) and Shahjahan Khan (Australia)

Received April 2, 2007; Revised August 5, 2007

References:



[1] J. Aitchison and I. R. Dunsmore, Statistical Prediction Analysis, Cambridge University Press, Cambridge, 1975.

[2] J. Aitchison and D. Sculthorpe, Some problems of statistical prediction, Biometrika 52 (1965), 469-483.

[3] J. T. Chien, A Bayesian prediction approach to robust speech recognition and online environment testing, Speech Communication 37 (2002), 321-334.

[4] G. D. Faulkenberry, A method of obtaining prediction intervals, J. Amer. Statist. Assoc. 68 (1973), 433-435.

[5] D. A. S. Fraser and M. S. Haq, Inference and prediction for multilinear model, J. Statist. Res. 4 (1970), 93-109.

[6] D. A. S. Fraser and K. W. Ng, Multivariate regression analysis with spherical error, Multivariate Analysis, V. P. R. Krishnaiah, ed., North-Holland Publishing Co., New York, 1980, pp. 369-386.

[7] S. Geisser, Predictive Inference: An Introduction, Chapman & Hall, London, 1993.

[8] A. S. Goldberger, Best linear unbiased prediction in the generalized linear regression model, J. Amer. Statist. Assoc. 57 (1962), 369-375.

[9] G. J. Hahn, Simultaneous prediction intervals for a regression model, Technometrics 14 (1972), 203-214.

[10] M. S. Haq, Structural relation and prediction for multivariate models, Statist. Hefte 23 (1982), 218-228.

[11] M. S. Haq and S. Khan, Prediction distribution for a linear regression model with multivariate Student-t error distribution, Comm. Statist. Theory Methods 19 (1990), 4705-4712.

[12] H. Jeffreys, Theory of Probability, 3rd ed., Oxford University Press, Oxford, 1961.

[13] S. Khan, Predictive inference for multilinear models with Student-t errors, Unpublished Ph.D. Thesis, Department of Statistical and Actuarial Sciences, The University of Western Ontario, Canada, 1992.

[14] S. Khan, Distribution of sum of squares and products for the generalized multilinear matrix-T model, J. Multivariate Anal. 83 (2002), 124-140.

[15] S. Khan, Predictive distribution of regression vector and residual sum of squares for normal multiple regression model, Comm. Statist. Theory. Methods 33 (2004), 2423-2441.

[16] S. Khan and M. S. Haq, Prediction inference for multilinear model with errors having multivariate Student-t distribution and first-order autocorrelation structure, Sankhya Ser. B 56 (1994), 95-106.

[17] S. Kotz and S. Nadarajah, Multivariate t Distributions and their Applications, Cambridge University Press, New York, 2004.

[18] H. V. Roberts, Probabilistic prediction, J. Amer. Statist. Assoc. 60 (1965), 50-62.

[19] B. C. Sutradhar and M. M. Ali, A generalization of the Wishart distribution for the elliptical model and its moments or the multivariate-t model, J. Multivariate Anal. 29 (1989), 155-162.

[20] A. L. Wilson, An approach to simultaneous tolerance interval in regression, Ann. Math. Statist. 38 (1967), 1536-1540.

[21] A. Zellner, An Introduction to Bayesian Inference in Econometrics, John Wiley & Sons, Inc., New York, 1971.

[22] A. Zellner, Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms, J. Amer. Statist. Assoc. 71 (1976), 400-405.

[23] A. Zellner and V. K. Chetty, Prediction and decision problems in regression models from the Bayesian point of view, J. Amer. Statist. Assoc. 60 (1965), 608-616.

Keywords and phrases: multiple regression model, multivariate Student-t errors, Bayesian method, uniform prior, prediction distribution, beta, univariate and multivariate Student-t distributions.

Communicated by Andrew Rosalsky

 


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