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Frequentist size of Bayesian inequality tests

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  • David M. Kaplan

    () (Department of Economics, University of Missouri)

  • Longhao Zhuo

Abstract

Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (e.g., Gaussian). For the corresponding limit 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 (sometimes strictly); and in other cases, size may be above, below, or equal to alpha. Two examples illustrate our results: testing stochastic dominance and testing curvature of a translog cost function.

Suggested Citation

  • David M. Kaplan & Longhao Zhuo, 2015. "Frequentist size of Bayesian inequality tests," Working Papers 1802, Department of Economics, University of Missouri, revised 26 Feb 2018.
  • Handle: RePEc:umc:wpaper:1802
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    References listed on IDEAS

    as
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    Cited by:

    1. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles or CDF values," Working Papers 16-19, Department of Economics, University of Missouri, revised 22 Feb 2018.

    More about this item

    Keywords

    Bernstein-von Mises theorem; convexity; first-order stochastic dominance; limit experiment; nonstandard inference;

    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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