Una prueba de independencia completa basada en la FDR
A test for complete Independence based on FDR
Abstract (en)
Analysis and interpretation of multivariate data is largely facilitated if the variables are independent. In the practice, this supposition is verified through a test for complete independence. We propose a new test for complete independence based on the false discovery rate (FDR), and report the results of a simulation study which compares the real significance levels of this proposal and other tests generally used. We found that the real significance level only remains under the theoretical one for the test based on FDR, and that this is regardless the size of the sample and number of variables. Finally, we illustrate our proposal with two examples.
Abstract (es)
References
Anderson, E. (1935), ‘The irises of the Gaspe peninsula’, Bulletin of the American Iris Society 59, 2–5.
Bartlett, M. (1954), ‘A note on multiplying factors for various χ 2 approximations’, Journal of the Royal Statistical Society, Ser. B (Methodological) 16, 296–298.
Benjamini, Y. & Hochberg, Y. (1995), ‘Controlling the false discovery rate: A practical and powerful approach to multiple testing’, Journal of the Royal Statistial Society, Series B (Methodological) 57(1), 389–400.
Box, G. (1949), ‘A general distribution theory for a class of likelihood criteria’, Biometrika 36, 317–346.
Correa, J. C. (2006), Control de la proporción de hipótesis rechazadas equivocadamente, Curso de Estad´ıstica Genética, Universidad de Antioquia.
Correa, J. C. (2011), ‘Diagnósticos de regresión usando la FDR (Tasa de Descubrimientos Falsos)’, Comunicaciones en Estad´ıstica 3(2), 109–118.
Dudoit, S., Yang, Y.-H., Callow, M. J. & Speed, T. P. (2002), ‘Statistical methods for identifying differentially expressed genes in replicated cDNA experiments’, Statistica Sinica 12, 111–139.
Morrison, D. F. (1976), Multivariate statistical methods, 2 edn, New York: McGraw-Hill.
Morrison, D. F. (2005), Multivariate statistical methods, 4 edn, Belmont, CA: Brooks/Cole.
Mudholkar, G. S., Trivedi, M. C. & Lin, T. (1982), ‘An approximation to the distribution of the likelihood ratio statistic for testing complete independence’, Technometrics 24(2), 139–143.
Nguyen, D. V., Bulak Apart, A., Wang, N. & Carrol, R. J. (2002), ‘DNA microarray experiments: biological and technological aspects’, Biometrics 58, 701–717.
R Core Team (2013), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.*http://www.R-project.org/
Schaffer, J. P. (1995), ‘Multiple hypothesis testing: A review’, Annu. Rev. Psychol. 46, 561–84.
Schott, J. R. (2005), ‘Testing for complete independence in high dimensions’, Biometrika 92(4), 951–956.
Wilks, S. S. (1935), ‘On the independence of k sets of normally distributed statistical variables’, Econometrika 3, 309–26.
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