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

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  • Shimizu, Hiroaki
  • Wakaki, Hirofumi
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 6 (July)
    Pages: 1080-1089

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:1080-1089

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    Keywords: Asymptotic expansion Class of test statistics General covariance structure Non-null distribution Local alternative Power comparison Linear structure Sphericity test;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
    2. 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.
    3. A. Swain, 1975. "A class of factor analysis estimation procedures with common asymptotic sampling properties," Psychometrika, Springer, vol. 40(3), pages 315-335, September.
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