del Barrio, Eustasio; Cuesta-Albertos, Juan A.; Matrán, Carlos Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests. (With comments). (English) Zbl 0997.62034 Test 9, No. 1, 1-96 (2000). Summary: 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. Cited in 3 ReviewsCited in 21 Documents MSC: 62G10 Nonparametric hypothesis testing 62G30 Order statistics; empirical distribution functions 62G20 Asymptotic properties of nonparametric inference 60F15 Strong limit theorems Keywords:empirical processes; correlation tests; Cramer von Mises; quantile processes; Kolmogorov-Smirnov; Shapiro-Wilk; goodness-of-fit tests; Wasserstein distance PDFBibTeX XMLCite \textit{E. del Barrio} et al., Test 9, No. 1, 1--96 (2000; Zbl 0997.62034) Full Text: DOI References: [1] Ali, M.M. (1974). Stochastic ordering and kurtosis measure.Journal of the American Statistical Association.69, 543–545. · Zbl 0292.62005 [2] Anderson, T.W. and D.A. Darling (1952). Asymptotic theory of certain ”goodness of fit” criteria based on stochastic processes.Annals of Mathematical Statistics,23, 193–212. · Zbl 0048.11301 [3] Araujo, A. and E. Giné (1980).The Central Limit Theorem for Real and Banach Valued Random Variables. 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