scholarly journals Testing the Multivariate Regular Variation Model

2020 ◽  
pp. 1-13
Author(s):  
John H. J. Einmahl ◽  
Fan Yang ◽  
Chen Zhou
Keyword(s):  
Regular Variation ◽  
Multivariate Regular Variation ◽  
Variation Model

Almost sure limit sets of random samples in ℝd

1988 ◽  
Vol 20 (3) ◽  
pp. 573-599 ◽  
Author(s):  
Richard A. Davis ◽  
Edward Mulrow ◽  
Sidney I. Resnick
Keyword(s):  
Regular Variation ◽  
Almost Sure Convergence ◽  
Random Sets ◽  
Regularity Conditions ◽  
Limit Set ◽  
Multivariate Regular Variation ◽  
Exponential Form ◽  
Limit Sets ◽  
Random Samples ◽  
Distribution Tail

If {Xj, } is a sequence of i.i.d. random vectors in , when do there exist scaling constants bn > 0 such that the sequence of random sets converges almost surely in the space of compact subsets of to a limit set? A multivariate regular variation condition on a properly defined distribution tail guarantees the almost sure convergence but without certain regularity conditions surprises can occur. When a density exists, an exponential form of regular variation plus some regularity guarantees the convergence.

scholarly journals Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation

2013 ◽  
Vol 45 (01) ◽  
pp. 139-163 ◽  
Author(s):  
Bikramjit Das ◽  
Abhimanyu Mitra ◽  
Sidney Resnick
Keyword(s):  
Classical Theory ◽  
Regular Variation ◽  
Environmental Science ◽  
Asymptotic Model ◽  
Multivariate Regular Variation ◽  
Tail Risk ◽  
Risk Estimates ◽  
Hidden Regular Variation ◽  
Definition Of

Multivariate regular variation plays a role in assessing tail risk in diverse applications such as finance, telecommunications, insurance, and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This problem can be partly ameliorated by using hidden regular variation (see Resnick (2002) and Mitra and Resnick (2011)). We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of tail risk regions.

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