Artículo Original
Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry
Publicado 2004-09-16
Palabras clave
- Compound symmetry,
- distribution; likelihood ratio test,
- intraclass correlation,
- null moments
Cómo citar
Castañeda, M. E., & Nagar, D. K. (2004). Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry. Revista Integración, Temas De matemáticas, 22(1 y 2), 59–66. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/512
Resumen
The non-null distribution of the modified likelihood ratio test statistic Λ∗ for testing multisample compound symmetry of q multivariate Gaussian models is derived. The non-null moments of Λ∗ are obtained in terms of Lauricella's hypergeometric function. The non-null distribution is expressed in terms of H-function.
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Referencias
[1]T. W. Anderson.An Introduction to Multivariate Statistical Analysis, 2ndEdition, John Wiley & Sons, New York, 1984.
[2]A. K. GuptaandD. K. Nagar. “Nonnull distribution of the likelihood ratiocriterion for testing equality of covariance matrices under intraclass correlationmodel”.Communications in Statistics-Theory and Methods,16(1987), no. 11,3323–3341.
[3]A. K. GuptaandD. K. Nagar.Matrix Variate Distributions, Chapman &Hall/CRC, Boca Raton, 2000.
[4]A. M. MathaiandR. K. Saxena.TheH-Function with Applications inStatistics and Other Disciplines, Halsted Press [John Wiley & Sons], New York-London-Sidney, 1978.
[5]D. K. Nagar,S. K. JainandA. K. Gupta. “On testing circular station-arity and related models”.Journal of Statistical Computation and Simulation,29(1988), no. 3, 225–239.
[6]D. K. NagarandM. E. Castañeda. “Testing multisample compound sym-metry”.Advances and Applications in Statistics,3(2003), no. 3, 285–292.
[7] D. K. NagarandC. C. Sánchez. “Exact percentage points for testingmultisample sphericity in the bivariate case”.Communications in Statistics-Simulation and Computation,33(2004), no. 2, 447–457.
[8]D. K. Nagar, J. ChenandA. K. Gupta. “Distribution and percentage pointsof the likelihood ratio statistic for testing circular symmetry”.ComputationalStatistics and Data Analysis,47(2004), no. 1, 79–89.
[9]D. K. Nagar, E. ZarrazolaandE. Bedoya. “Percentage points for testingintraclass correlation structure”.Journal of Probability and Statistical Science,2(2004), no. 2, 199–211.
[10]I. OlkinandS. J. Press. “Testing and estimation for a circular stationarymodel”.Annals of Mathematical Statistics,40(1969), 1358–1373.
[11]H. M. SrivastavaandP. W. Karlsson.Multiple Gaussian HypergeometricSeries, John Wiley & Sons, New York, 1985.
[12]David F. Votaw. “Testing compound symmetry in a normal multivariate dis-tribution”.Annals of Mathematical Statistics,19(1948), 447-473.
[13]S. S. Wilks. “Sample criteria for testing equality of means, equality of variancesand equality of covariances in a normal multivariate distribution”.Annals ofMathematical Statistics,17(1946), 257–281.
[2]A. K. GuptaandD. K. Nagar. “Nonnull distribution of the likelihood ratiocriterion for testing equality of covariance matrices under intraclass correlationmodel”.Communications in Statistics-Theory and Methods,16(1987), no. 11,3323–3341.
[3]A. K. GuptaandD. K. Nagar.Matrix Variate Distributions, Chapman &Hall/CRC, Boca Raton, 2000.
[4]A. M. MathaiandR. K. Saxena.TheH-Function with Applications inStatistics and Other Disciplines, Halsted Press [John Wiley & Sons], New York-London-Sidney, 1978.
[5]D. K. Nagar,S. K. JainandA. K. Gupta. “On testing circular station-arity and related models”.Journal of Statistical Computation and Simulation,29(1988), no. 3, 225–239.
[6]D. K. NagarandM. E. Castañeda. “Testing multisample compound sym-metry”.Advances and Applications in Statistics,3(2003), no. 3, 285–292.
[7] D. K. NagarandC. C. Sánchez. “Exact percentage points for testingmultisample sphericity in the bivariate case”.Communications in Statistics-Simulation and Computation,33(2004), no. 2, 447–457.
[8]D. K. Nagar, J. ChenandA. K. Gupta. “Distribution and percentage pointsof the likelihood ratio statistic for testing circular symmetry”.ComputationalStatistics and Data Analysis,47(2004), no. 1, 79–89.
[9]D. K. Nagar, E. ZarrazolaandE. Bedoya. “Percentage points for testingintraclass correlation structure”.Journal of Probability and Statistical Science,2(2004), no. 2, 199–211.
[10]I. OlkinandS. J. Press. “Testing and estimation for a circular stationarymodel”.Annals of Mathematical Statistics,40(1969), 1358–1373.
[11]H. M. SrivastavaandP. W. Karlsson.Multiple Gaussian HypergeometricSeries, John Wiley & Sons, New York, 1985.
[12]David F. Votaw. “Testing compound symmetry in a normal multivariate dis-tribution”.Annals of Mathematical Statistics,19(1948), 447-473.
[13]S. S. Wilks. “Sample criteria for testing equality of means, equality of variancesand equality of covariances in a normal multivariate distribution”.Annals ofMathematical Statistics,17(1946), 257–281.