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Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests

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Abstract

This paper analyzes the evolution of the asymptotic theory of goodness-of-fit tests. We emphasize the parallel development of this theory and the theory of empirical and quantile processes. Our study includes the analysis of the main tests of fit based on the empirical distribution function, that is, tests of the Cramér-von Mises or Kolmogorov-Smirnov type. We pay special attention to the problem of testing fit to a location scale family. We provide a new approach, based on the Wasserstein distance, to correlation and regression tests, outlining some of their properties and explaining their limitations.

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Authors and Affiliations

  1. Departmento dd Estadística e Investigación Operativa, Universidad de Valladolid, Spain

    Eustasio del Barrio

  2. Departmento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Spain

    Juan A. Cuesta-Albertos

  3. Departmento de Estadística, Facultad de Ciencias, Universidad de Valladolid, 47005, Valladolid, Spain

    Carlos Matrán

  4. University of Szeged, Hungary

    Sándor Csörgö

  5. Universitat de Barcelona, Spain

    Carles M. Cuadras

  6. University of Stellenbosch, South, Africa

    Tertius de Wet

  7. University of Connecticut, USA

    Evarist Giné

  8. Simon Fraser University, Canada

    Richard Lockhart

  9. Ruhr-Universität Bochum and Universtität Siegen, Germany

    Axel Munk

  10. University of Giessen, Germany

    Winfried Stute

Authors
  1. Eustasio del Barrio
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  2. Juan A. Cuesta-Albertos
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  3. Carlos Matrán
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  4. Sándor Csörgö
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  5. Carles M. Cuadras
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  6. Tertius de Wet
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  7. Evarist Giné
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  8. Richard Lockhart
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  9. Axel Munk
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  10. Winfried Stute
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Additional information

Dedicated to Miguel Martín Díaz whose scientific criticism has greatly inspirated our research by years.

Research partially supported by DGICYT, grants PB98-0369-C02-01 and 02. E. del barrio and C. Matrán have also been supproted by PAPIJCL grant VA08/97.

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del Barrio, E., Cuesta-Albertos, J.A., Matrán, C. et al. Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests. Test 9, 1–96 (2000). https://doi.org/10.1007/BF02595852

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