Hidden Regular Variation and Detection of Hidden Risks

Abstract

Hidden regular variation requires regular variation on 𝔼 = [0, ∞] ^d  \ {(0, 0,…, 0)} and another regular variation on the sub-cone , where 𝕃 _i is the ith axis. We extend this concept to sub-cones of 𝔼⁽²⁾ as well. We suggest a procedure for detecting hidden regular variation, and when it exists, propose a method of estimating the limit measure exploiting its semi-parametric structure. We give an example where hidden regular variation yields improved estimates of probabilities of risk sets.

Keywords:

• Regular variation
• Risk sets
• Spectral measure
• Vague convergence
• Weak convergence

Mathematics Subject Classification:

• 62GB32
• 91B30
• 91B70

ACKNOWLEDGMENT

S. I. Resnick and A. Mitra were partially supported by ARO Contract W911NF-10-1-0289 at Cornell University.