Asymptotic independence and support detection techniques for heavy-tailed multivariate data
| Autor: | Jaakko Lehtomaa, Sidney I. Resnick |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics, Survival and event history analysis |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
HIDDEN REGULAR VARIATION Economics and Econometrics Multivariate statistics Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Power law Set (abstract data type) 010104 statistics & probability Multivariate regular variation Dimension (vector space) Asymptotic independence DEPENDENCE NONPARAMETRIC-ESTIMATION 0502 economics and business Statistics Consistent estimator 111 Mathematics FOS: Mathematics Test statistic EXTREMOGRAM 512 Business and Management 0101 mathematics 90A46 91B30 60G70 60K10 62F05 62G32 Heavy-tailed POWER-LAW DISTRIBUTIONS Risk management 050205 econometrics Mathematics business.industry 05 social sciences Support estimation Estimator SPECTRAL MEASURE COEFFICIENT Statistics Probability and Uncertainty business SET BEHAVIOR |
| Popis: | One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently independent. This paper aims to help to identify asymptotically independent risks by providing additional tools for describing dependence structures of multiple risks when the individual risks can obtain very large values. The study is performed in the setting of multivariate regular variation. We show how asymptotic independence is connected to properties of the support of the angular measure and present an asymptotically consistent estimator of the support. The estimator generalizes to any dimension $N\geq 2$ and requires no prior knowledge of the support. The validity of the support estimate can be rigorously tested under mild assumptions by an asymptotically normal test statistic. 40 pages, 8 figures |
| Databáze: | OpenAIRE |
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