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June 2018 Testing Un-Separated Hypotheses by Estimating a Distance
Jean-Bernard Salomond
Bayesian Anal. 13(2): 461-484 (June 2018). DOI: 10.1214/17-BA1059


In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to test for. This is shown to be equivalent to a modification of the testing loss. An advantage of this approach is that it can easily be adapted to complex hypotheses testing which are in general difficult to test for. Asymptotic properties of the test can be derived from the asymptotic behaviour of the posterior distribution of the discrepancy measure, and gives insight on possible calibrations. In addition one can derive separation rates for testing, which ensure the asymptotic frequentist optimality of our procedures.


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Jean-Bernard Salomond. "Testing Un-Separated Hypotheses by Estimating a Distance." Bayesian Anal. 13 (2) 461 - 484, June 2018.


Published: June 2018
First available in Project Euclid: 23 June 2017

zbMATH: 06989956
MathSciNet: MR3780431
Digital Object Identifier: 10.1214/17-BA1059


Vol.13 • No. 2 • June 2018
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