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A new approach to construction of objective priors: Hellinger information

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  • Shemyakin, Arkady

    () (University of St. Thomas, St. Paul, USA)

Abstract

Non-informative priors play crucial role in objective Bayesian analysis. Most popular ways of construction of non-informative priors are provided by the Jeffreys rule, matching probability principle, and reference prior approach. An alternative construction of non-informative priors is suggested based on the concept of Hellinger information related to Hellinger distance. Under certain regularity conditions, limit behavior of the Hellinger distance as the difference in the parameter values goes down to zero is closely related to Fisher information. In this case our approach generalizes the Jeffreys rule. However, what is more interesting, Hellinger information can be also used to describe information properties of the parametric set in non-regular situations, when Fisher information does not exist. Non-informative priors based on Hellinger information are studied for the non-regular class of distributions defined by Ghosal and Samanta and for some interesting examples outside of this class.

Suggested Citation

  • Shemyakin, Arkady, 2012. "A new approach to construction of objective priors: Hellinger information," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 28(4), pages 124-137.
  • Handle: RePEc:ris:apltrx:0199
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    File URL: http://pe.cemi.rssi.ru/pe_2012_4_124-137.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    Cited by:

    1. repec:nea:journl:y:2017:i:36:p:12-30 is not listed on IDEAS
    2. Slutskin, Lev, 2015. "Definition of a prior distribution in Bayesian analysis by minimizing Kullback–Leibler divergence under data availability," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 40(4), pages 129-141.

    More about this item

    Keywords

    non-informative priors; reference priors; Jeffreys’ rule; Hellinger distance; Hellinger information.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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