Bayesian and frequentist tests of sign equality and other nonlinear inequalities

David Kaplan

No 1516, Working Papers from Department of Economics, University of Missouri

Abstract: Testing whether two parameters have the same sign is a nonstandard problem due to the non-convex shape of the parameter subspace satisfying the composite null hypothesis, which is a nonlinear inequality constraint. We describe a simple example where the ordering of likelihood ratio (LR), Wald, and Bayesian sign equality tests reverses the "usual" ordering: the Wald rejection region is a subset of LR's, as is the Bayesian rejection region (either asymptotically or with an uninformative prior). Under general conditions, we show that non-convexity of the null hypothesis subspace is a necessary but not sufficient condition for this asymptotic frequentist/Bayesian ordering. Since linear inequalities only generate convex regions, a corollary is that frequentist tests are more conservative than Bayesian tests in that setting. We also examine a nearly similar-on-the-boundary, unbiased test of sign equality. Rather than claim moral superiority of one statistical framework or test, we wish to clarify the regrettably ineluctable tradeoffs.

Keywords: convexity; likelihood ratio; limit experiment; nonstandard inference; unbiased test; Wald (search for similar items in EconPapers)
JEL-codes: C11 C12 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2015-07-14
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (5)

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Related works:
Working Paper: Frequentist size of Bayesian inequality tests (2019)
Working Paper: Frequentist properties of Bayesian inequality tests (2019)
Working Paper: Frequentist size of Bayesian inequality tests (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:umc:wpaper:1516

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