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Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests |
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| Authors: | Eustasio del Barrio Juan A. Cuesta-Albertos Carlos Matrán Sándor Csörgö Carles M. Cuadras Tertius de Wet Evarist Giné Richard Lockhart Axel Munk Winfried Stute |
| Affiliation: | 1. Departmento dd Estadística e Investigación Operativa, Universidad de Valladolid, Spain 2. Departmento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Spain 3. Departmento de Estadística, Facultad de Ciencias, Universidad de Valladolid, 47005, Valladolid, Spain 4. University of Szeged, Hungary 5. Universitat de Barcelona, Spain 6. University of Stellenbosch, South, Africa 7. University of Connecticut, USA 8. Simon Fraser University, Canada 9. Ruhr-Universit?t Bochum and Universtit?t Siegen, Germany 10. University of Giessen, Germany |
| 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. 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. |
| Keywords: | Goodness-of-fit correlation tests Cramér-von Mises empirical and quantile/processes Kolmogorov-Smirnov Shapiro-Wilk strong approximations Wasserstein distance |
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