The central limit theorem on spaces of positive definite matrices

Donald St P. Richards

doi:10.1016/0047-259X(89)90031-6

The central limit theorem on spaces of positive definite matrices

Donald St P. Richards

Statistics

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Abstract

A central limit theorem is obtained for orthogonally invariant random variables on P_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).

Original language	English (US)
Pages (from-to)	326-332
Number of pages	7
Journal	Journal of Multivariate Analysis
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/0047-259X(89)90031-6
State	Published - May 1989

All Science Journal Classification (ASJC) codes

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/0047-259X(89)90031-6

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title = "The central limit theorem on spaces of positive definite matrices",

abstract = "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).",

author = "Richards, \{Donald St P.\}",

note = "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.",

year = "1989",

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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

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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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DO - 10.1016/0047-259X(89)90031-6

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -

The central limit theorem on spaces of positive definite matrices

Abstract

All Science Journal Classification (ASJC) codes

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