NDLI: Nonparametric estimation of the spectral measure, and associated dependence measures, for multivariate extreme values using a limiting conditional representation

Content Provider	Springer Nature Link
Author	Eastoe, Emma F. Heffernan, Janet E. Tawn, Jonathan A.
Copyright Year	2013
Abstract	The traditional approach to multivariate extreme values has been through the multivariate extreme value distribution G, characterised by its spectral measure H and associated Pickands’ dependence function A. More generally, for all asymptotically dependent variables, H determines the probability of all multivariate extreme events. When the variables are asymptotically dependent and under the assumption of unit Fréchet margins, several methods exist for the estimation of G, H and A which use variables with radial component exceeding some high threshold. For each of these characteristics, we propose new asymptotically consistent nonparametric estimators which arise from Heffernan and Tawn’s approach to multivariate extremes that conditions on variables with marginal values exceeding some high marginal threshold. The proposed estimators improve on existing estimators in three ways. First, under asymptotic dependence, they give self-consistent estimators of G, H and A; existing estimators are not self-consistent. Second, these existing estimators focus on the bivariate case, whereas our estimators extend easily to describe dependence in the multivariate case. Finally, for asymptotically independent cases, our estimators can model the level of asymptotic independence; whereas existing estimators for the spectral measure treat the variables as either being independent, or asymptotically dependent. For asymptotically dependent bivariate random variables, the new estimators are found to compare favourably with existing estimators, particularly for weak dependence. The method is illustrated with an application to finance data.
Starting Page	25
Ending Page	43
Page Count	19
File Format	PDF
ISSN	13861999
Journal	Extremes
Volume Number	17
Issue Number	1
e-ISSN	1572915X
Language	English
Publisher	Springer US
Publisher Date	2013-05-05
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asymptotic dependence Conditional distribution Economic monetary union Multivariate extreme value theory Nonparametric modelling Poisson process Statistics Quality Control, Reliability, Safety and Risk Civil Engineering Hydrogeology Environmental Management Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics, Econometrics and Finance Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Portfolio risk assessment using multivariate extreme value methods

Relations between the spectral measures and dependence of MEV distributions

Influence measures and robust estimators of dependence in multivariate extremes

Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles

Asymptotically (in)dependent multivariate maxima of moving maxima processes

A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values

Bivariate extreme-value copulas with discrete Pickands dependence measure

Transition kernels and the conditional extreme value model

Dependence Estimation and Visualization in Multivariate Extremes with Applications to Financial Data

Nonparametric estimation of the spectral measure, and associated dependence measures, for multivariate extreme values using a limiting conditional representation

Similar Documents

Portfolio risk assessment using multivariate extreme value methods

Relations between the spectral measures and dependence of MEV distributions

Influence measures and robust estimators of dependence in multivariate extremes

Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles

Asymptotically (in)dependent multivariate maxima of moving maxima processes

A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values

Bivariate extreme-value copulas with discrete Pickands dependence measure

Transition kernels and the conditional extreme value model

Dependence Estimation and Visualization in Multivariate Extremes with Applications to Financial Data

Nonparametric estimation of the spectral measure, and associated dependence measures, for multivariate extreme values using a limiting conditional representation