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Un prueba de Cucconi modificada para alternativas de cambio en localización y escala
A modified Cucconi Test for Location and Scale Change Alternatives
Keywords:
combinación de pruebas, modelo de localización y escala, pruebas de rangos (es)Combining tests, Location-scale model, Rank tests (en)
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1Università della Calabria, Dipartimento di Economia e Statistica, Italia. Professor. Email: mmarozzi@unical.it
The most common approach to develop a test for jointly detecting location and scale changes is to combine a test for location and a test for scale. For the same problem, the test of Cucconi should be considered because it is an alternative to the other tests as it is based on the squares of ranks and contrary-ranks. It has been previously shown that the Cucconi test is robust in level and is more powerful than the Lepage test, which is the most commonly used test for the location-scale problem. A modification of the Cucconi test is proposed. The idea is to modify this test consistently with the familiar approach which develops a location-scale test by combining a test for location and a test for scale. More precisely, we will combine the Cucconi test with the Wilcoxon rank test for location and a modified Levene test following the theory of the nonparametric combination. A power comparison of this modified Cucconi test with the original one, the Lepage test and the Podgor-Gastwirth PG2 test, shows that the modified Cucconi test is robust in size and markedly more powerful than the other tests for every considered type of distributions, from short- to normal- and long-tailed ones. A real data example is discussed.
Key words: Combining tests, Location-scale model, Rank tests.
La alternativa más común para implementar una prueba que detecta cambios en localización y escala conjuntamente es combinar una prueba de localización con una de escala. Para este problema, la prueba de Cucconi es considerada como una alternativa de otras pruebas que se basan en los cuadrados de los rangos y los contrarangos. Esta prueba es robusta en nivel y es más poderosa que la prueba de Lepage la cual es la más usada para el problema de localización-escala. En este artículo se propone una modificación de la prueba de Cucconi. La idea es modificar la prueba mediante la combinación de una prueba de localización y uno de escala. Mas precisamente, se sugiere combinar la prueba de Cucconi con la prueba de rangos de Wilcoxon para localizacion y una prueba modificada de Levene siguiendo la teoría de la combinación no paramétrica. Una comparación de la potencia de esta prueba modificada de Cucconi con la prueba original, la prueba de Lepage y la prueba PG2 de Podgor-Gastwirth muestran que la prueba de Cucconi modificada es robusta en tamaño y mucho más poderosa que las anteriores para todas las distribuciones consideradas desde la normal hasta algunas de colas largas. Se hace una aplicación a datos reales.
Palabras clave: combinación de pruebas, modelo de localización y escala, pruebas de rangos.
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References
1. Brown, M. B. & Forsythe, A. B. (1974), 'Robust tests for the equality of variantes', Journal of the American Statistical Association 69, 364-367.
2. Conover, W. J., Johnson, M. E. & Johnson, M. M. (1981), 'A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data', Technometrics 23, 351-361.
3. Cucconi, O. (1968), 'Un nuovo test non parametrico per il confronto tra due gruppi campionari', Giornale degli Economisti 27, 225-248.
4. Good, P. (2000), Permutation Tests, a Practical Guide to Resampling Methods for Testing Hypotheses, 2 edn, Springer-Verlag, New York.
5. Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J. & Ostrowski, E. (1994), A Handbook Of Small Data Sets, Chapman and Hall, London.
6. Hollander, M. & Wolfe, D. A. (1999), Nonparametric Statistical Methods, 2 edn, Wiley, New York.
7. Lepage, Y. (1971), 'A combination of Wilcoxon and Ansari-Bradley statistics', Biometrika 58, 213-217.
8. Marozzi, M. (2004a), 'A bi-aspect nonparametric test for the multi-sample location problem', Computational Statistics and Data Analysis 46, 81-92.
9. Marozzi, M. (2004b), 'A bi-aspect nonparametric test for the two-sample location problem', Computational Statistics and Data Analysis 44, 639-648.
10. Marozzi, M. (2007), 'Multivariate tri-aspect non-parametric testing', Journal of Nonparametric Statistics 19, 269-282.
11. Marozzi, M. (2009), 'Some notes on the location-scale Cucconi test', Journal of Nonparametric Statistics 21, 629-647.
12. Marozzi, M. (2011), 'Levene type tests for the ratio of two scales', Journal of Statistical Computation and Simulation 81, 815-826.
13. Marozzi, M. (2012), 'Combined interquantile range tests for differences in scale', Statistical Papers 53, 61-72.
14. Perng, S. K. & Littel, R. C. (1976), 'A test of equality of two normal population means and variances', Journal of the American Statistical Association 71, 968-971.
15. Pesarin, F. (2001), Multivariate Permutation Tests With Applications In Biostatistics, Wiley, Chichester.
16. Pesarin, F. & Salmaso, S. (2010), Permutation Tests for Complex Data, Wiley, Chichester.
17. Podgor, M. J. & Gastwirth, J. L. (1994), 'On non-parametric and generalized tests for the two-sample problem with location and scale change alternatives', Statistics in Medicine 13, 747-758.
18. Snedecor, G. W. & Cochran, W. G. (1989), Statistical Methods, 8 edn, Iowa State University Press, Ames.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n3a03,
AUTHOR = {Marozzi, Marco},
TITLE = {{A modified Cucconi Test for Location and Scale Change Alternatives}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {3},
pages = {371-384}
}
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