The Probability Content of Cones in Isotropic Random Fields
AbstractThis paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 66 (1998)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Osiewalski, J. & Steel, M.F.J., 1990.
"Robust Bayesian inference in elliptical regression models,"
1990-32, Tilburg University, Center for Economic Research.
- Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
- Osiewalski, J. & Steel, M., 1990. "Robust Bayesian Inference In Elliptical Regression Models," Papers 9032, Tilburg - Center for Economic Research.
- Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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