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The central limit theorem on spaces of positive definite matrices

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  • Richards, Donald St. P.

Abstract

A central limit theorem is obtained for orthogonally invariant random variables on n, the space of n - n real, positive definite symmetric matrices. The derivation requires the Taylor expansion of the spherical functions for the general linear group GL(n, R). This extends from the case n = 3 a result of Terras (J. Multivariate Anal. 23 (1987), 13-36).

Suggested Citation

  • Richards, Donald St. P., 1989. "The central limit theorem on spaces of positive definite matrices," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 326-332, May.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:2:p:326-332
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    Cited by:

    1. P. Sawyer, 2001. "The Central Limit Theorem on SO0(p, q)/SO(p)×SO(q)," Journal of Theoretical Probability, Springer, vol. 14(3), pages 857-866, July.
    2. Michael Voit, 2017. "Dispersion and Limit Theorems for Random Walks Associated with Hypergeometric Functions of Type BC," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1130-1169, September.

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