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Reference Priors for the General Location-Scale Model

Author

Listed:
  • Fernández, C.
  • Steel, M.F.J.

    (Tilburg University, Center For Economic Research)

Abstract

The reference prior algorithm (Berger and Bernardo 1992) is applied to multivariate location-scale models with any regular sampling density, where we establish the irrelevance of the usual assumption of Normal sampling if our interest is in either the location or the scale. This result immediately extends to the linear regression model. On the other hand, an essentially arbitrary step in the reference prior algorithm, namely the choice of the nested sequence of sets in the parameter space is seen to play a role. Our results lend an additional motivation to the often used prior proportional to the inverse of the scale parameter, as it is found to be both the independence Jeffreys' prior and the reference prior under variation independence in the sequence of sets, for any choice of the sampling density. However, if our parameter of interest is not a one-to-one transformation of either location or scale, the choice of the sampling density is generally shown to intervene.
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Suggested Citation

  • Fernández, C. & Steel, M.F.J., 1997. "Reference Priors for the General Location-Scale Model," Discussion Paper 1997-105, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:3a91a072-b14c-4c07-b2e7-0780503efe41
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    References listed on IDEAS

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    1. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Inference under Sampling from Scale Mixtures of Normals," Discussion Paper 1996-02, Tilburg University, Center for Economic Research.
    2. Y. Yang, 1995. "Invariance of the reference prior under reparametrization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 83-94, June.
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    Cited by:

    1. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    2. Soumya Roy & Biswabrata Pradhan, 2023. "Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 208-232, May.
    3. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    4. Bodnar, Olha & Eriksson, Viktor, 2021. "Bayesian model selection: Application to adjustment of fundamental physical constants," Working Papers 2021:7, Örebro University, School of Business.

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