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Predictivistic characterizations of multivariate student-t models

Author

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  • Loschi, Rosangela H.
  • Iglesias, Pilar L.
  • Arellano-Valle, Reinaldo B.

Abstract

De Finetti style theorems characterize models (predictive distributions) as mixtures of the likelihood function and the prior distribution, beginning from some judgment of invariance about observable quantities. The likelihood function generally has its functional form identified from invariance assumptions only. However, we need additional conditions on observable quantities (typically, assumptions on conditional expectations) to identify the prior distribution. In this paper, we consider some well-known invariance assumptions and establish additional conditions on observable quantities in order to obtain a predictivistic characterization of the multivariate and matrix-variate Student-t distributions as well as for the Student-t linear model. As a byproduct, a characterization for the Pearson type II distribution is provided.

Suggested Citation

  • Loschi, Rosangela H. & Iglesias, Pilar L. & Arellano-Valle, Reinaldo B., 2003. "Predictivistic characterizations of multivariate student-t models," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 10-23, April.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:10-23
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    References listed on IDEAS

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    1. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    2. R. Arellano-Valle & H. Bolfarine & P. Iglesias, 1994. "A predictivistic interpretation of the multivariatet distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 221-236, December.
    3. Rosangela Loschi & Pilar Iglesias & Rinaldo Arellano-Valle, 2002. "Conditioning on uncertain event: Extensions to bayesian inference," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 365-383, December.
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    1. Loschi, R.H. & Iglesias, P.L. & Arellano-Valle, R.B. & Cruz, F.R.B., 2007. "Full predictivistic modeling of stock market data: Application to change point problems," European Journal of Operational Research, Elsevier, vol. 180(1), pages 282-291, July.
    2. 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.
    3. M. Arashi & A. Saleh & S. Tabatabaey, 2010. "Estimation of parameters of parallelism model with elliptically distributed errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 79-100, January.
    4. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.

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