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March 2016 Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions
Miriam Isabel Seifert
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J. Appl. Probab. 53(1): 130-145 (March 2016).

Abstract

By considering the extreme behavior of bivariate random vectors with a polar representation R(u(T), v(T)), it is commonly assumed that the radial component R and the angular component T are stochastically independent. We investigate how to relax this rigid independence assumption such that conditional limit theorems can still be deduced. For this purpose, we introduce a novel measure for the dependence structure and present convenient criteria for validity of limit theorems possessing a geometrical meaning. Thus, our results verify a stability of the available limit results, which is essential in applications where the independence of the polar components is not necessarily present or exactly fulfilled.

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Miriam Isabel Seifert. "Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions." J. Appl. Probab. 53 (1) 130 - 145, March 2016.

Information

Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1337.60026
MathSciNet: MR3471952

Subjects:
Primary: 60F05
Secondary: 60G70, 62E20, 62G32

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 1 • March 2016
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