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<p>The underlying idea of equivalence tests is to validate approximate models rather than merely rejecting them. This paper studies a test designed to confirm whether an observed multinomial dataset can be modelled by a parametric family using a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>-divergence as a measure of dissimilarity. The critical value is determined from the asymptotic normality of the test statistic. The asymptotic correctness and consistency of the proposed method are theoretically proved. The test’s performance in finite samples is studied via simulation. Furthermore, to illustrate the usefulness of the test, a parametric multinomial model for the risk preferences of experimental subjects is validated.</p>

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Equivalence tests for multinomial data with composite null hypothesis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月20日

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  • M. V. Alba-Fernández,
  • M. D. Jiménez-Gamero,
  • F. Jiménez-Jiménez

摘要

The underlying idea of equivalence tests is to validate approximate models rather than merely rejecting them. This paper studies a test designed to confirm whether an observed multinomial dataset can be modelled by a parametric family using a \(\phi \) ϕ -divergence as a measure of dissimilarity. The critical value is determined from the asymptotic normality of the test statistic. The asymptotic correctness and consistency of the proposed method are theoretically proved. The test’s performance in finite samples is studied via simulation. Furthermore, to illustrate the usefulness of the test, a parametric multinomial model for the risk preferences of experimental subjects is validated.