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Bayesian inference for the correlation coefficient in two seemingly unrelated regressions

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  • Wang, Min
  • Sun, Xiaoqian

Abstract

We study the problems of hypothesis testing and point estimation for the correlation coefficient between the disturbances in the system of two seemingly unrelated regression equations. An objective Bayesian solution to each problem is proposed based on combined use of the invariant loss function and the objective prior distribution for the unknown model parameters. It is shown that this new solution possesses an invariance property under monotonic reparameterization of the quantity of interest. The performance of the proposed solution is examined through a simulation study. Furthermore, the solution is illustrated by an application to the real annual data for analyzing the investment model.

Suggested Citation

  • Wang, Min & Sun, Xiaoqian, 2012. "Bayesian inference for the correlation coefficient in two seemingly unrelated regressions," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2442-2453.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2442-2453
    DOI: 10.1016/j.csda.2012.01.021
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    References listed on IDEAS

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    1. G. Datta & J. Ghosh, 1995. "Noninformative priors for maximal invariant parameter in group models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 95-114, June.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    3. Fraser, D.A.S. & Rekkas, M. & Wong, A., 2005. "Highly accurate likelihood analysis for the seemingly unrelated regression problem," Journal of Econometrics, Elsevier, vol. 127(1), pages 17-33, July.
    4. José M. Bernardo & Raúl Rueda, 2002. "Bayesian Hypothesis Testing: a Reference Approach," International Statistical Review, International Statistical Institute, vol. 70(3), pages 351-372, December.
    5. José Bernardo, 2005. "Intrinsic credible regions: An objective Bayesian approach to interval estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 317-384, December.
    6. Liu, Aiyi, 2002. "Efficient Estimation of Two Seemingly Unrelated Regression Equations," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 445-456, August.
    7. Wang, Lichun & Lian, Heng & Singh, Radhey S., 2011. "On efficient estimators of two seemingly unrelated regressions," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 563-570, May.
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