Weighted quantile correlation tests for Gumbel, Weibull and Pareto families

• Autorzy: Csörgõ S. , Szabó T.
• Języki publikacji: EN

Abstrakty

EN

Weighted quantile correlation tests are worked out for the Gumbel location and location-scale families. Our theoretical emphasis is on the determination of computable forms of the asymptotic distributions under the null hypotheses, which forms are based on the solution of an associated eigenvalue-eigenfunction problem. Suitable transformations then yield corresponding composite goodness-of-fit tests for the Weibull family with unknown shape and scale parameters and for the Pareto family with an unknown shape parameter. Simulations demonstrate slow convergence under the null hypotheses, and hence the inadequacy of the asymptotic critical points. Other rounds of extensive simulations illustrate the power of all three tests: Gumbel against the other extreme-value distributions, Weibull against gamma distributions, and Pareto against generalized Pareto distributions with logarithmic slow variation.

Słowa kluczowe

EN

composite goodness of fit; Gumbel, Weibull and Pareto families; weighted quantile correlation tests; asymptotic distribution; speed of convergence; power

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2009
• Tom: Vol. 29, Fasc. 2
• Strony: 227--250
• Opis fizyczny: Bibliogr. 18 poz., tab., wykr.

Twórcy

autor

Csörgõ S.

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

autor

Szabó T.

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

Bibliografia

• [1] A. Cabaña and A. J. Quiroz, Using the empirical moment generating function in testing for the Weibull and the Type I extreme value distribution, Test 13 (2005), pp. 417-431.
• [2] S. Csörgõ, Testing for Weibull scale families as a test case for Wasserstein correlation tests (Discussion of [7]), Test 9 (2000), pp. 54-70.
• [3] S. Csörgõ, Weighted correlation tests for scale families, Test 11 (2002), pp. 219-248.
• [4] S. Csörgõ, Weighted correlation tests for location-scale families, Math. Comput. Modelling 38 (2003), pp. 753-762.
• [5] S. Csörgõ and T. Szabó, Weighted correlation tests for gamma and lognormal families, Tatra Mt. Math. Publ. 26 (2003), pp. 337-356.
• [6] E. del Barrio, J. A. Cuesta-Albertos and C. Matrán, Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests (With discussion), Test 9 (2000), pp. 1-96.
• [7] E. del Barrio, J. A. Cuesta-Albertos, C. Matrán and J. M. Rodríguez-Rodríguez, Tests of goodness of fit based on the L2-Wasserstein distance, Ann. Statist. 27 (1999), pp. 1230-1239.
• [8] E. del Barrio, E. Giné and F. Utzet, Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances, Bernoulli 11 (2005), pp. 131-189.
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• [10] T. de Wet, Goodness-of-fit tests for location and scale families based on a weighted L2-Wasserstein distance measure, Test 11 (2002), pp. 89-107.
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• [13] É. Krauczi, A study of the quantile correlation test for normality, Test 16 (2009), to appear.
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Uwagi

In memoriam Professor Béla Gyires (1909–2001)