Use of Spherical Harmonics in Testing for Elliptical
Symmetry.
ABSTRACT:
Spherical Harmonics have been succesfully used in
statistical procedures for testing multivariate normality (Quiroz and Dudley,
1991, Manzotti and Quiroz, 2001). The purpose of this talk is to explain
how these polynomials can be used in tests for the composite, infinite
dimensional null hypothesis of elliptical symmetry, for which few testing
procedures exist. A nice feature of the method is that the statistics
obtained have an exact limiting chi-squared distribution (independently
of the particular parametric family to which the data belong
within the elliptically symmetric distributions), and, as our simulations
show, the finite sample quantiles converge rather rapidly to their limiting
values. We evaluate, in simulations, the power of one of the
statistics presented against different forms of departure from the null
hypothesis in the bivariate setting.
About the Speaker
Dr. Quiroz is currently visiting McMaster from Simon Bolivar University
in Caracas, Venezuala. He received his Ph.D. from MIT in 1986 under the
direction of Richard M. Dudley and then held a postdoctoral position at Bell
Communications Research for two years. Since then he has worked at
Simon Bolivar Univeristy. His main research interests lie in statistical
applications of empirical processes and methods of graph theory in statistics.
References
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Beran, R. (1979) Testing for ellipsoidal symmetry of a multivariate
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Fang, K.T., Kotz, S. and Ng, K.W. (1990) Symmetric Multivariate and
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Monographs on Statistics and Applied Probability 36
Chapman and Hall, London.
Heathcote, C. R., Rachev, S. T. and Cheng, B. (1995) Testing
multivariate symmetry.
Journal of Multivariate Analysis, 54, 91-112.
Koltchinskii, V. I. and Li, L. (1998) Testing for spherical symmetry
of a multivariate distribution.
Journal of Multivariate Analysis, 65, 228-244.
Quiroz, A. J. and Dudley, R. M. (1991)
Some New Tests for Multivariate Normality
Probability Theory and Related Fields87, 521-546.
