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Frequentist properties of Bayesian inequality tests

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  • David M. Kaplan

    () (Department of Economics, University of Missouri)

  • Longhao Zhuo

Abstract

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist size of a certain Bayesian hypothesis test of (possibly nonlinear) inequalities. If the null hypothesis is that the (possibly infinite-dimensional) parameter lies in a certain half-space, then the Bayesian test's size is alpha; if the null hypothesis is a subset of a half-space, then size is above alpha; and in other cases, size may be above, below, or equal to alpha. Rejection probabilities at certain points in the parameter space are also characterized. Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships.

Suggested Citation

  • David M. Kaplan & Longhao Zhuo, 2019. "Frequentist properties of Bayesian inequality tests," Working Papers 1910, Department of Economics, University of Missouri.
  • Handle: RePEc:umc:wpaper:1910
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    Cited by:

    1. David M. Kaplan & Longhao Zhuo, 2018. "Comparing latent inequality with ordinal data," Working Papers 1816, Department of Economics, University of Missouri, revised Feb 2019.
    2. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    3. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.

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    More about this item

    Keywords

    generalized Bayes rule; limit experiment; minimax; nonstandard inference; posterior;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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