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Asymptotic expansions for a class of tests for a general covariance structure under a local alternative


  • Shimizu, Hiroaki
  • Wakaki, Hirofumi


Let be a pxp random matrix having a Wishart distribution . For testing a general covariance structure , we consider a class of test statistics , where is a distance measure from to , [lambda]i's are the eigenvalues of , and h is a given function with certain properties. Wakaki, Eguchi and Fujikoshi (1990) suggested this class and gave an asymptotic expansion of the null distribution of Th. This paper gives an asymptotic expansion of the non-null distribution of Th under a sequence of alternatives. By using results, we derive the power, and compare the power asymptotically in the class. In particular, we investigate the power of the sphericity tests.

Suggested Citation

  • Shimizu, Hiroaki & Wakaki, Hirofumi, 2011. "Asymptotic expansions for a class of tests for a general covariance structure under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1080-1089, July.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:1080-1089

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    References listed on IDEAS

    1. A. Swain, 1975. "A class of factor analysis estimation procedures with common asymptotic sampling properties," Psychometrika, Springer;The Psychometric Society, vol. 40(3), pages 315-335, September.
    2. Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
    3. Wakaki, Hirofumi & Eguchi, Shinto & Fujikoshi, Yasunori, 1990. "A class of tests for a general covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 313-325, February.
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