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Original Articles

Exact Nonnull Distributions of Sphericity Tests for Trivariate Normal Population with Power Comparison

Pages 355-374 | Published online: 14 Aug 2013

  • CarterE.M. and SrivastavaM.S.(1977). Monotonicity of the power functions of modified likelihood ratio criterion for the homogeneity of variances and of the sphericity test. J. Multivariate Anal. 7 229–233.
  • ChanY.M. and SrivastavaM.S.(1988). Comparison of powers for the sphericity tests using both the asymptotic distribution and the bootstrap. Commun. Statist.-Theory Meth. 17 (3) 671–690.
  • Grieve, A.P.(1984). Tests of sphericity of normal distributions and the analysis of repeated measures designs. Psychometrika 49 257–267.
  • HarrisP. and PeersH.W.(1980). The local power of the efficient scores test statistic. Biometrika 67 525–529.
  • JamesA.T.(1968). Calculation of zonal polynomial coefficients by use of the Laplace- Beltrami operator. Ann. Math. Statist. 39 1711–1718.
  • JohnS.(1971). Some optimal multivariate tests. Biometrika 58 123–127.
  • JohnS.(1972). The distribution of a statistic used for testing sphericity of normal distributions. Biometrika 59 169–173.
  • JohnS.(1976). Fitting Sampling distribution agreeing in support and moments and table of critical values of sphericity criterion. J. Multivariate. Anal. 6 601–607.
  • KhatriC.G. and SrivastavaM.S.(1971). On exact non-null distributions of likelihood ratio criteria for sphericity test and equality of two covariance matrices. Sankhyā Ser.A, 33 201–206.
  • NagaoH.(1973). On some test criteria for covariance matrix. Ann. Statist. 1 700–709.
  • NagaoH.(1973). Asymptotic expansions of the distributions of Bartlett's test and sphericity test under local alternatives. Ann. Inst. Statist. Math. 25 407–422.
  • NagaoH.(1974). Asymptotic nonnull distributions of certain test criteria for a covariance matrix. J. Multivariate Anal. 4 409–418.
  • NagaoN.(1989). Tests of hypotheses for covariance matrices and distributions under multivariate normal populations. Amer. J. Math, and Management Sci. 9 31–49.
  • NagaoH.(1993). Asymptotic expansions of some test criteria for sphericity test and test of independence under local alternatives from an elliptical distribution. Math. Japonica 38 165–170.
  • NagaoH. and SrivastavaM.S.(1992). On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations. J. Multivariate Anal. 43 331–350.
  • Nagarsenker(1976). Exact non-null distribution of the likelihood ratio criteria for covariance matrix. Canadian J. Statist. 4 237–254.
  • Nagarsenker and Pillai(1973). The distribution of the sphericity test criterion. J. Multivariate Anal. 3 226–234.
  • SugiuraN.(1969). Asymptotic expansions of the distributions of the likelihood ratio criteria for covariance matrix. Ann. Math. Statist. 40 2051–2063.
  • SugiuraN.(1972). Locally best invariant test for sphericity and the limiting distributions. Ann. Math. Statist. 43 1312–1316.

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