On the regular variation of elliptical random vectors

Enkelejd Hashorva

Statistics & Probability Letters, 2006, vol. 76, issue 14, 1427-1434

Abstract: Let S=(S1,...,Sd)[inverted perpendicular],d[greater-or-equal, slanted]2 be a spherical random vector in and let X=A[inverted perpendicular]S be an elliptical random vector with a non-singular matrix. Berman (1992. Sojourns and Extremes of Stochastic Processes. Wadsworth & Brooks/Cole) proved that if the random radius is regularly varying with index [alpha]>0 then S and Si,1[less-than-or-equals, slant]i[less-than-or-equals, slant]d are regularly varying with index [alpha]. In this paper we derive several new equivalent conditions for the regular variation of X. As a by-product we obtain two asymptotic results concerning the sojourn and supremum of Berman processes.

Keywords: Regularly; varying; vectors; Elliptical; random; vectors; Berman; process; Sojourn; limit; theorem; Asymptotics; of; supremum; Coefficient; of; upper; tail; dependence (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (8)

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