https://doi.org/10.15446/rce.v38n1.48805
1Chongju University, Department of Statistics, Chongju, South Korea. Professor. Email: hipark@cju.ac.kr
In this research we propose several nonparametric simultaneous test procedures for location and scale parameters. We construct test statistics based on linear rank statistics choosing a suitable combining function. We obtain the overall p-values by applying the permutation principle. We compare the efficiency amongst combining functions by obtaining empirical powers through a simulation study. We discuss some interesting aspects of our procedure as concluding remarks.
Key words: Combining function, Multi-aspect Test, Permutation Principle, Two-sample Location-scale Problem.
En este artículo se propone un procedimiento de pruebas simultáneas no paramétricas para los paramétros de localización y escala. Se construyen los estadísticos de prueba basados en los estadísticos de rangos lineales para las subhipótesis nulas con la escogencia de una adecuada función de combinación; se obtienen los valores p al aplicar el principio de permutación; se compara la eficiencia entre las funciones de combinación mediante la obtención de las potencias empíricas a través de un estudio de simulación y por último se discuten algunos aspectos interesantes del procedimiento como conclusiones.
Palabras clave: funciones de combinación, parámetro de escala, parámetro de localización, principio de permutación, problema de dos muestras, pruebas simultáneas.
Texto completo disponible en PDF
References
1. Ansari, A. R. & Bradley, R. A. (1960), 'Rank-sum tests for dispersions', Annals of Mathematical Statistics 31, 1174-1189.
2. Brombin, C., Salmaso, L., Ferronato, G. & Galzignato, P.-F. (2011), 'Multi-aspect procedures for paired data with application to biometric morphing', Communications in Statistics-Simulation and Computation 40, 1-12.
3. Duran, B. S., Tsai, W. S. & Lewis, T. O. (1976), 'A class of location-scale nonparametric tests', Biometrika 63, 173-176.
4. Efron, B. (1979), 'Bootstrap methods: Another look at the jackknife', Annals of Statistics 7, 1-26.
5. Fisher, R. A. (1932), Statistical Methods for Research Workers, 4 edn, Oliver & Boyd, Edinburgh.
6. Fleming, T. R., Harrington, D. P. & O'Sullivan, M. (1987), 'Supremum version of the logrank and generalized ilcoxon statistics', Journal of the American Statistical Association 82, 312-320.
7. Good, P. (2000), Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypotheses, 2 edn, Springer, New York.
8. Lepage, Y. (1971), 'A combination of Wilcoxon's and Ansari-Bradley's statistics', Biometrika 58, 213-217.
9. Lepage, Y. (1973), 'A table for a combined Wilcoxon Ansari-Bradley statistic', Biometrika 60, 113-116.
10. Liptak, I. (1958), 'On the combination of independent tests', Magyar Tudomanyos Akademia Matematikai Kutato Intezenek Kozlomenyei 3, 127-141.
11. Marozzi, M. (2004), 'A bi-aspect nonparametric test for the two-sample location problem', Computational Statistics and Data Analysis 44, 639-648.
12. Marozzi, M. (2007), 'Multivariate tri-aspect non-parametric testing', Journal of Nonparametric Statistics 19, 269-282.
13. Marozzi, M. (2009), 'Some notes on the location-scale Cucconi test', Journal of Nonparametric Statistics 21, 629-647.
14. Marozzi, M. (2012a), 'A modified Cucconi test for location and scale change alternatives', Revista Colombiana de Estadistica 35, 371-384.
15. Marozzi, M. (2012b), 'A distribution free test for the equality of scales', Communications in Statistics-Simulation and Computation 41, 878-889.
16. Marozzi, M. (2012b), 'A modified Hall-Padmanabhan test for the homogeneity of scales', Communications in Statistics-Theory and Methods 41, 3068-3078.
17. Marozzi, M. (2012b), 'A combined test for differences in scale based on the interquantile range', Statistical Papers 53, 61-72.
18. Marozzi, M. (2013), 'Nonparametric simultaneous tests for location and scale testing: A comparison of several methods', Communications in Statistics-Simulation and Computation 42, 1298-1317.
19. Marozzi, M. (2014), 'The multisample Cucconi test', Statistical Methods and Applications 23(2), 209-227.
20. Mood, A. M. (1954), 'On the asymptotic efficiency of certain nonparametric two-sample tests', Annals of Mathematical Statistics 25, 514-522.
21. Murakami, H. (2007), 'Lepage type statistic based on the modified Baumgartner statistic', Computational Statistics and Data Analysis 51, 5061-5067.
22. Neuhäuser, M., Leuchs, A.-K. & Ball, D. (2011), 'A new location-scale test based on a combination of the ideas of Levene and Lepage', Biometrical Journal 53(3), 525-534.
23. Park, H. I. (2011), 'A nonparametric test procedure based on a group of quantile tests', Communications in Statistics-Simulation and Computation 40, 759-783.
24. Pesarin, F. (2001), Multivariate Permutation Tests, Wiley, Chichester.
25. Pesarin, F. & Salmaso, L. (2010), Permutation Tests for Complex Data, Wiley, Chichester.
26. Pettitt, A. N. (1976), 'A two-sample Anderson-Darling rank statistic', Biometrika 63, 161-168.
27. 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.
28. Randles, R. H. & Hogg, R. V. (1971), 'Certain uncorrelated and independent rank statistics', Journal of American Statistical Association 66, 569-574.
29. Randles, R. H. & Wolfe, D. A. (1979), Introduction to the Theory of Nonparametric Statistics, Wiley, New York.
30. Rublik, F. (2009), 'Critical values for testing location-scale hypothesis', Measurement Science Review 9, 9-15.
31. Salmaso, L. & Solari, A. (2005), 'Multiple aspect testing for case-control designs', Metrika 62, 331-340.
32. Shao, J. & Tu, D. (1995), The Jackknife and Bootstrap, Springer, New York.
33. Tippett, L. H. C. (1931), The Methods of Statistics, Williams and Norgate, London.
34. Zhang, J. (2006), 'Powerful two-sample tests based on the likelihood ratio', Technometrics 48, 95-103.
35. van Zwet, W. R. & Oostherhoff, J. (1967), 'On the combination of independent test statistics', Annals of Mathematical Statistics 38, 659-680.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv38n1a06,
AUTHOR = {Park, Hyo-Il},
TITLE = {{Nonparametric Simultaneous Test Procedures}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2015},
volume = {38},
number = {1},
pages = {107-121}
}