Nonparametric Simultaneous Test Procedures

• HYO-IL PARK ^[1]
  1. [1] Chongju University Department of Statistics
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 38, Nº. 1, 2015, págs. 107-121
• Idioma: inglés
• DOI: 10.15446/rce.v38n1.48805
• Títulos paralelos:
  • Procedimientos de pruebas simultáneas no paramétricas
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Ansari, A. R.,Bradley, R. A.. (1960). 'Rank-sum tests for dispersions'. Annals of Mathematical Statistics. 31. 1174-1189
  • Brombin, C.,Salmaso, L.,Ferronato, G.,Galzignato, P.-F.. (2011). 'Multi-aspect procedures for paired data with application to biometric...
  • Duran, B. S.,Tsai, W. S.,Lewis, T. O.. (1976). 'A class of location-scale nonparametric tests'. Biometrika. 63. 173-176
  • Efron, B.. (1979). 'Bootstrap methods: Another look at the jackknife'. Annals of Statistics. 7. 1-26
  • Fisher, R. A.. (1932). Statistical Methods for Research Workers. 4. Oliver & Boyd.
  • Fleming, T. R.,Harrington, D. P.,O'Sullivan, M.. (1987). 'Supremum version of the logrank and generalized ilcoxon statistics'....
  • Good, P.. (2000). Permutation Tests-A Practical Guide to Resampling Methods for Testing Hypotheses. 2. Springer.
  • Lepage, Y.. (1971). 'A combination of Wilcoxon's and Ansari-Bradley's statistics'. Biometrika. 58. 213-217
  • Lepage, Y.. (1973). 'A table for a combined Wilcoxon Ansari-Bradley statistic'. Biometrika. 60. 113-116
  • Liptak, I.. (1958). 'On the combination of independent tests'. Magyar Tudomanyos Akademia Matematikai Kutato Intezenek Kozlomenyei....
  • Marozzi, M.. (2004). 'A bi-aspect nonparametric test for the two-sample location problem'. Computational Statistics and Data Analysis....
  • Marozzi, M.. (2007). 'Multivariate tri-aspect non-parametric testing'. Journal of Nonparametric Statistics. 19. 269-282
  • Marozzi, M.. (2009). 'Some notes on the location-scale Cucconi test'. Journal of Nonparametric Statistics. 21. 629-647
  • Marozzi, M.. (2012). 'A modified Cucconi test for location and scale change alternatives'. Revista Colombiana de Estadistica. 35....
  • Marozzi, M.. (2012). 'A distribution free test for the equality of scales'. Communications in Statistics-Simulation and Computation....
  • Marozzi, M.. (2012). 'A modified Hall-Padmanabhan test for the homogeneity of scales'. Communications in Statistics-Theory and Methods....
  • Marozzi, M.. (2012). 'A combined test for differences in scale based on the interquantile range'. Statistical Papers. 53. 61-72
  • Marozzi, M.. (2013). 'Nonparametric simultaneous tests for location and scale testing: A comparison of several methods'. Communications...
  • Marozzi, M.. (2014). 'The multisample Cucconi test'. Statistical Methods and Applications. 23. 209-227
  • Mood, A. M.. (1954). 'On the asymptotic efficiency of certain nonparametric two-sample tests'. Annals of Mathematical Statistics....
  • Murakami, H.. (2007). 'Lepage type statistic based on the modified Baumgartner statistic'. Computational Statistics and Data Analysis....
  • Neuhäuser, M.,Leuchs, A.-K.,Ball, D.. (2011). 'A new location-scale test based on a combination of the ideas of Levene and Lepage'....
  • Park, H. I.. (2011). 'A nonparametric test procedure based on a group of quantile tests'. Communications in Statistics-Simulation...
  • Pesarin, F.. (2001). Multivariate Permutation Tests. Wiley.
  • Pesarin, F.,Salmaso, L.. (2010). Permutation Tests for Complex Data. Wiley.
  • Pettitt, A. N.. (1976). 'A two-sample Anderson-Darling rank statistic'. Biometrika. 63. 161-168
  • Podgor, M. J.,Gastwirth, J. L.. (1994). 'On non-parametric and generalized tests for the two-sample problem with location and scale change...
  • Randles, R. H.,Hogg, R. V.. (1971). 'Certain uncorrelated and independent rank statistics'. Journal of American Statistical Association....
  • Randles, R. H.,Wolfe, D. A.. (1979). Introduction to the Theory of Nonparametric Statistics. Wiley.
  • Rublik, F.. (2009). 'Critical values for testing location-scale hypothesis'. Measurement Science Review. 9. 9-15
  • Salmaso, L.,Solari, A.. (2005). 'Multiple aspect testing for case-control designs'. Metrika. 62. 331-340
  • Shao, J.,Tu, D.. (1995). The Jackknife and Bootstrap. Springer.
  • Tippett, L. H. C.. (1931). The Methods of Statistics. Williams and Norgate.
  • Zhang, J.. (2006). 'Powerful two-sample tests based on the likelihood ratio'. Technometrics. 48. 95-103
  • van Zwet, W. R.,Oostherhoff, J.. (1967). 'On the combination of independent test statistics'. Annals of Mathematical Statistics. 38....