TY - JOUR
T1 - The central limit theorem on spaces of positive definite matrices
AU - Richards, Donald St P.
N1 - Funding Information:
Received March 1988; revised April 1988. AMS 1980 subject classifications: 43A65, 6OFO2, 62E15. Key words and phrases: spherical functions, central limit theorem, symmetric spaces, Helgason-Fourier transform, heat equation, orthogonal group, zonal polynomials. * Supported in part by the National Science Foundation Grant DMS-8601671; current address: Department of Mathematics, Mathematics-Astronomy Building, University of Virginia, Charlottesville, VA 22903.
PY - 1989/5
Y1 - 1989/5
N2 - A central limit theorem is obtained for orthogonally invariant random variables on Pn, 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).
AB - A central limit theorem is obtained for orthogonally invariant random variables on Pn, 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).
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U2 - 10.1016/0047-259X(89)90031-6
DO - 10.1016/0047-259X(89)90031-6
M3 - Article
AN - SCOPUS:38249022473
SN - 0047-259X
VL - 29
SP - 326
EP - 332
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 2
ER -