, Volume 20, Issue 4, pp 873–904 | Cite as

Hidden regular variation under full and strong asymptotic dependence



Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the data tends to concentrate along particular directions and does not cover the full space. This is observed in various data sets from finance, insurance, network traffic, social networks, etc. In this paper we discuss the notions of full and strong asymptotic dependence for bivariate data along with the idea of hidden regular variation in these cases. In a risk analysis setting, this leads to improved risk estimation accuracy when regular methods provide a zero estimate of risk. Analyses of both real and simulated data sets illustrate concepts of generation and detection of such models.


Regular variation Multivariate heavy tails Hidden regular variation Tail estimation Strong dependence 

AMS 2000 Subject Classifications

28A33 60G70 62G05 62G32 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Engineering Systems and DesignSingapore University of Technology and DesignSingaporeSingapore
  2. 2.School of ORIECornell UniversityIthacaUSA

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