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Activity Number:
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387
- Software
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Type:
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Contributed
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Date/Time:
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Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
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Sponsor:
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Section on Statistical Computing
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Abstract #319088
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Title:
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Optimal Equivalence Testing in Exponential Families
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Author(s):
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Robert Paige* and Renren Zhao
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Companies:
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Missouri S&T and College of Coastal Georgia
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Keywords:
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equivalence tests;
exponential families;
saddlepoint approximations;
uniformly most powerful tests
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Abstract:
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We consider the development of a UMPU equivalence testing procedure for a difference in canonical parameters of a regular exponential family. This development involves a non-unique interest parameter preserving (IPP) reparametrization. In our development we show that the underlying conditional exponential family, for the difference parameter, is invariant under the choice of IPP transformation. Most often it is the case that the conditional exponential family for the difference parameter is intractable. We reproduce this conditional distribution to a high degree of accuracy using Skovgaard's saddlepoint approximation and show that the resulting saddlepoint-based testing procedure is invariant to the choice of IPP reparametrization. We consider the practically important problem of equivalence testing for two independent normal samples. We develop six competing equivalence testing procedures for the mean-to-variance ratio. Simulation studies which show that our procedure outperforms all competing methods by exhibiting an empirical significance level which does not differ significantly from the nominal 5% rate.
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Authors who are presenting talks have a * after their name.
