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# Frequentist size of Bayesian inequality tests

## Author

Listed:
• David M. Kaplan

(University of Missouri)

• Longhao Zhuo

(Bank of America)

## 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, 2016. "Frequentist size of Bayesian inequality tests," Papers 1607.00393, arXiv.org, revised Feb 2018.
• Handle: RePEc:arx:papers:1607.00393
as

File URL: http://arxiv.org/pdf/1607.00393

## References listed on IDEAS

as
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Full references (including those not matched with items on IDEAS)

## Citations

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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.

### 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

### NEP fields

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