Testing Equality of Several Correlation Matrices

• ARJUN K. GUPTA ^[1] ; BRUCE E. JOHNSON ^[3] ; DAYA K. NAGAR ^[2]
  1. [1] Bowling Green State University

     Bowling Green State University

     City of Bowling Green, Estados Unidos

     
  2. [2] Universidad de Antioquia

     Universidad de Antioquia

     Colombia

     
  3. [3] Experient Research Group

  Mostrar afiliaciones +
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 36, Nº. 2, 2013, págs. 237-258
• Idioma: inglés
• Títulos paralelos:
  • Prueba de igualdad de varias matrices de correlación
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo se muestra que el estadístico L* de Kullback, para probar la igualdad de varias matrices de correlación, puede ser considerado como un estadístico modificado del test de razón de verosimilitud cuando se muestrean poblaciones normales multivariadas. Derivamos la distribución asintótica nula de L* en series que involucran variables independientes chi-cuadrado, mediante la expansión de L* en términos de otras variables aleatorias y luego invertir la expansión término a término. Se da también un ejemplo para mostrar el procedimiento a ser usado cuando se prueba igualdad de matrices de correlación mediante el estadístico L*.

  • English

    In this article we show that the Kullbacks statistic for testing equality of several correlation matrices may be considered a modified likelihood ratio statistic when sampling from multivariate normal populations. We derive the asymptotic null distribution of L* in series involving independent chi-square variables by expanding L* in terms of other random variables and then inverting the expansion term by term. An example is also given to exhibit the procedure to be used when testing the equality of correlation matrices using the statistic L\ast.

• Referencias bibliográficas
  • Aitkin, M. A.,Nelson, W. C.,Reinfurt, K. H.. (1968). 'Tests for correlation matrices'. Biometrika. 55. 327-334
  • Aitkin, M.. (1969). 'Some tests for correlation matrices'. Biometrika. 56. 443-446
  • Ali, M. M.,Fraser, D. A. S.,Lee, Y. S.. (1970). 'Distribution of the correlation matrix'. Journal of Statistical Research. 4. 1-15
  • Anderson, T. W.. (2003). An Introduction to Multivariate Statistical Analysis. Wiley-Interscience [John Wiley & Sons]. Hoboken.
  • Browne, M. W.. (1978). 'The likelihood ratio test for the equality of correlation matrices'. The British Journal of Mathematical and...
  • Cole, N.. (1968). On testing the equality of correlation matrices. The L. L. Thurstone Psychometric Laboratory, University of North Carolina....
  • Cole, N.. (1968). The likelihood ratio test of the equality of correlation matrices. The L. L. Thurstone Psychometric Laboratory, University...
  • Gleser, L. J.. (1968). 'On testing a set of correlation coefficients for equality: Some asymptotic results'. Biometrika. 55. 513-517
  • Gupta, A. K.,Johnson, B. E.,Nagar, D. K.. (2012). Testing equality of several correlation matrices. Department of Mathematics and Statistics,...
  • Gupta, A. K.,Nagar, D. K.. (2000). Matrix Variate Distributions. Chapman & Hall/CRC, Boca Raton, FL.
  • Gupta, A. K.,Varga, T.. (1993). Elliptically Contoured Models in Statistics. Kluwer Academic Publishers Group.
  • Jennrich, R. I.. (1970). 'An asymptotic \chi\sp{2} test for the equality of two correlation matrices'. Journal of the American Statistical...
  • Kaplan, E. L.. (1952). 'Tensor notation and the sampling cumulants of k-statistics'. Biometrika. 39. 319-323
  • Kendall, M. G.,Stuart, A.. (1969). The Advanced Theory of Statistics. Hafner Publishing Co., New York.
  • Konishi, S.. (1978). 'An approximation to the distribution of the sample correlation coefficient'. Biometrika. 65. 654-656
  • Konishi, S.. (1979). 'Asymptotic expansions for the distributions of functions of a correlation matrix'. Journal of Multivariate Analysis....
  • Konishi, S.. (1979). 'Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in principal component...
  • Konishi, S.,Sugiyama, T.. (1981). 'Improved approximations to distributions of the largest and the smallest latent roots of a Wishart...
  • Kullback, S.. (1967). 'On testing correlation matrices'. Applied Statistics. 16. 80-85
  • Kullback, S.. (1997). Information Theory and Statistics. Dover Publications Inc.. Mineola.
  • Modarres, R.. (1993). 'Testing the equality of dependent variances'. Biometrical Journal. 35. 785-790
  • Modarres, R.,Jernigan, R. W.. (1992). 'Testing the equality of correlation matrices'. Communications in Statistics. Theory and Methods....
  • Modarres, R.,Jernigan, R. W.. (1993). 'A robust test for comparing correlation matrices'. Journal of Statistical Computation and Simulation....
  • Muirhead, R. J.. (1982). Aspects of Multivariate Statistical Theory. John Wiley & Sons Inc..
  • Schott, J. R.. (2007). 'Testing the equality of correlation matrices when sample correlation matrices are dependent'. Journal of Statistical...
  • Siotani, M.,Hayakawa, T.,Fujikoshi, Y.. (1985). Modern Multivariate Statistical Analysis: A Graduate Course and Handbook. American Sciences...
  • Waternaux, C. M.. (1984). 'Principal components in the nonnormal case: The test of equality of q roots'. Journal of Multivariate Analysis....