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Objective Bayesian analysis for a truncated model

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  • Wang, Haiying
  • Sun, Dongchu

Abstract

In this paper, the reference prior is developed for a truncated model with boundaries of support as two functions of an unknown parameter. It generalizes the result obtained in a recent paper by Berger et al. (2009), in which a rigorous definition of reference priors was proposed and the prior for a uniform distribution with parameter-dependent support was derived. The assumption on the order of the derivatives of these two boundary functions, required by Berger et al. (2009), is removed. In addition, we obtain the frequentist asymptotic distribution of Bayes estimators under the squared error loss function. Comparisons of the Bayesian approach with the frequentist approach are drawn in two examples in detail. Both theoretical and numerical results indicate that the Bayesian approach, especially under the reference prior, is preferable.

Suggested Citation

  • Wang, Haiying & Sun, Dongchu, 2012. "Objective Bayesian analysis for a truncated model," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2125-2135.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2125-2135
    DOI: 10.1016/j.spl.2012.07.013
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    References listed on IDEAS

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    1. Ghosal Subhashis & Samanta Tapas, 1997. "Expansion Of Bayes Risk For Entropy Loss And Reference Prior In Nonregular Cases," Statistics & Risk Modeling, De Gruyter, vol. 15(2), pages 129-140, February.
    2. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
    3. S. Ghosal, 1997. "Reference priors in multiparameter nonregular cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 159-186, June.
    4. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, September.
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    1. Ferreira, Paulo H. & Ramos, Eduardo & Ramos, Pedro L. & Gonzales, Jhon F.B. & Tomazella, Vera L.D. & Ehlers, Ricardo S. & Silva, Eveliny B. & Louzada, Francisco, 2020. "Objective Bayesian analysis for the Lomax distribution," Statistics & Probability Letters, Elsevier, vol. 159(C).

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