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Optimal equivalence testing in exponential families

Author

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  • Renren Zhao

    (College of Coastal Georgia)

  • Robert L. Paige

    (Missouri University of Science and Technology)

Abstract

We develop uniformly most powerful unbiased (UMPU) two sample equivalence test for a difference of canonical parameters in exponential families. This development involves a non-unique reparametrization. We address this issue via a novel characterization of all possible reparametrizations of interest in terms of a matrix group. Furthermore, our procedure involves an intractable conditional distribution which we reproduce to a high degree of accuracy using saddlepoint approximations. The development of this saddlepoint-based procedure involves a non-unique reparametrization but we show that our procedure is invariant under choice of reparametrization. Our real data example considers the mean-to-variance ratio for normally distributed data. We compare our result to six competing equivalence testing procedures for the mean-to-variance ratio. Only our UMPU method finds evidence of equivalence, which is the expected result. We also perform a Monte Carlo simulation study which shows that our UMPU method outperforms all competing methods by exhibiting an empirical significance level which is not statistically significantly different from the nominal 5% level for all simulation settings.

Suggested Citation

  • Renren Zhao & Robert L. Paige, 2023. "Optimal equivalence testing in exponential families," Statistical Papers, Springer, vol. 64(5), pages 1507-1525, October.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01346-4
    DOI: 10.1007/s00362-022-01346-4
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    References listed on IDEAS

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    1. Robert L. Paige & A. Alexandre Trindade & P. Harshini Fernando, 2009. "Saddlepoint‐Based Bootstrap Inference for Quadratic Estimating Equations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 98-111, March.
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