Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

Bernoulli

Volumn 11, Issue 1, 2005, Pages 131-189

  Del Barrio, Eustasio ^a   Gine, Evarist ^b   Utzet, Frederic ^c  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Distributional limit theorems; Tests of fit to location scale families; Weighted L2 norms of the quantile process; Weighted wasserstein distance

Indexed keywords

EID: 33845652549     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1110228245     Document Type: Article

References (21)

1. Araujo, A. and Giné, E. (1980) The Central Limit Theorem for Real and Banach Valued Random Variables. New York: Wiley
2. Bickel, P. and Freedman, D. (1981) Some asymptotic theory for the bootstrap. Ann Statist., 9, 1196-1216.
3. p norms of weighted uniform empirical and quantile processes. Ann. Probab., 16, 142-161.
4. Csörgö, M. and Horváth, L. (1993) Weighted Approximations in Probability and Statistics. New York: Wiley
5. Csörgö, M. and Révész, P. (1978) Strong approximations of the quantile process. Ann. Statist., 6, 882-894.
6. Csörgö, M., Csörgö, S., Horváth, L. and Mason, D.M. (1986) Weighted empirical and quantile processes. Ann. Probab., 14, 31-85.
7. Csörgö, S. (2000) Testing for Weibull scale families as a test case for Wasserstein correlation tests. Test, 9, 54-70. [Discussion to del Barrio et al. (2000).]
8. Csörg̈, S. (2002) Weighted correlation tests for scale families. Test, 11, 219-248.
9. Csörgö, S. (2003) Weighted correlation tests for location-scale families. Math. Comput. Modelling, 38, 753-762.
10. de la Peña, V and Giné, E. (1999) Decoupling: From Dependence to Independence. New York: Springer-Verlag.
11. de Wet, T. (2000) Discussion to del Barrio, Cuesta-Albertos and Matran (2000). Test, 9, 74-79.
12. 2Wasserstein distance measure. Test, 11, 89-107.
13. de Wet, T. and Venter, J.H. (1972) Asymptotic distributions of certain test criteria of normality. South African Statist. J., 6, 135-149.
14. de Wet, T. and Venter, J.H. (1973) Asymptotic distributions for quadratic forms with applications to tests of fit. Ann. Statist., 1, 380-387.
15. del Barrio, E. (2001) An elementary derivation of the asymptotic distribution of statistics of Shapiro-Wilk type. Preprint.
16. 2-Wasserstein distance. Ann. Statist., 27, 1230-1239.
17. del Barrio, E., Giné, E and Matrán, C. (1999b) Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Ann. Probab., 27, 1009-1071.
18. del Barrio, E., Cuesta-Albertos, J. and Matrán, C. (2000) Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests. Test, 9, 1-96.
19. Dunford, N. and Schwartz, J.T. (1963) Linear Operators, Part II. New York: Wiley.
20. Gregory, G. (1997) Functions of order statistics and tests of fit. South African Statist. J., 11, 99-118.
21. Guttorp, P. and Lockhart, R.A. (1988) On the asymptotic distribution of quadratic forms in uniform order statistics. Ann. Statist., 16, 433-449.