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The distribution of the sphericity test criterion

Author

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  • Nagarsenker, B. N.
  • Pillai, K. C. S.

Abstract

The exact distribution of Mauchly's sphericity test criterion W = S/[trS/p]p, when S is the sum of product matrix from a sample of size N taken from a p-variate normal population, is obtained using contour integration and methods similar to those of Nair and Box. Tables of percentage points for p = 4(1)10, [alpha] = 0.01 and 0.05, and various values of N (including small) are given and comparisons made with approximate percentage points using methods of Box, Mauchly, Tukey and Wilks, and Davis.

Suggested Citation

  • Nagarsenker, B. N. & Pillai, K. C. S., 1973. "The distribution of the sphericity test criterion," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 226-235, June.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:2:p:226-235
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    Cited by:

    1. Ferre, Louis, 1995. "Selection of components in principal component analysis: A comparison of methods," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 669-682, June.
    2. Cho, Jin Seo & Phillips, Peter C.B., 2018. "Pythagorean generalization of testing the equality of two symmetric positive definite matrices," Journal of Econometrics, Elsevier, vol. 202(1), pages 45-56.
    3. Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.

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