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Nonparametric validation of similar distributions and assessment of goodness of fit

Author

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  • Axel Munk
  • Claudia Czado

Abstract

In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an α‐trimmed version of Mallows distance Γα(F, G) between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned Γα(F, G) neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence. It is shown that Γα(F, G) can be interpreted as average and population equivalence. Our approach is illustrated by various examples.

Suggested Citation

  • Axel Munk & Claudia Czado, 1998. "Nonparametric validation of similar distributions and assessment of goodness of fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 223-241.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:223-241
    DOI: 10.1111/1467-9868.00121
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    Cited by:

    1. Alvarez-Esteban, Pedro C. & del Barrio, Eustasio & Cuesta-Albertos, Juan A. & Matrán, Carlos, 2010. "Assessing when a sample is mostly normal," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2914-2925, December.
    2. Eustasio del Barrio & Hristo Inouzhe & Carlos Matrán, 2020. "Box-Constrained Monotone Approximations to Lipschitz Regularizations, with Applications to Robust Testing," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 65-87, October.
    3. Freitag, Gudrun & Munk, Axel, 2005. "On Hadamard differentiability in k-sample semiparametric models--with applications to the assessment of structural relationships," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 123-158, May.
    4. L. Baringhaus & N. Henze, 2017. "Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 167-188, April.
    5. Genest Christian & Scherer Matthias, 2019. "The world of vines: An interview with Claudia Czado," Dependence Modeling, De Gruyter, vol. 7(1), pages 169-180, January.
    6. E. Barrio & H. Inouzhe & C. Matrán, 2020. "On approximate validation of models: a Kolmogorov–Smirnov-based approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 938-965, December.
    7. Rippl, Thomas & Munk, Axel & Sturm, Anja, 2016. "Limit laws of the empirical Wasserstein distance: Gaussian distributions," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 90-109.
    8. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
    9. del Barrio, Eustasio & Gordaliza, Paula & Lescornel, Hélène & Loubes, Jean-Michel, 2019. "Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 341-362.

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