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Multivariate Extremes - Methodology
A Working
Group in Risk Analysis, Extreme Events and Decision Theory
Group Leaders: Richard Smith
Webmasters: Guang Cheng
Password Protected
Site (future)
Announcements
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News! 01/07/08, Spring semester meeting schedule: every Monday from
10:30-12:00, starting from 01/14/08 01/07/08, No meeting on 01/21/08. Meeting Time: Thursday 9:30 - 11:00 Working Groups Dial-in & WebEx Instructions Group Email: mvmeth-risk AT samsi DOT info |
Meeting Activities
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Date |
Topics & Readings |
Notes |
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Suggested reading list:
Summary of 09/27 Meeting: We agreed
that, rather than focus on published books and papers with no clear objective
in view, it was better to formulate specific problems. After further
discussion, we fixed the following four: 1.
Multivariate extensions of the Ledford-Tawn approach. [This was suggested by
me in response to a specific challenge to propose a theoretical problem. The
background is that Ledford and Tawn, JRSSB 1997, proposed an approach to
bivariate extremes that significantly extends the traditional method based on
bivariate extreme value distributions. But it has not, to my knowledge, been
extended to d>2. I think there is considerable potential for that, or to
look at other closely related problems.] 2.
Multivariate extremes in climatic data. [This was thought to be a good topic
because of the ready availability of data, the interests of several members
of the group, and the rich potential for problems, e.g. including both
spatial and temporal dependence, multivariate in the sense of looking at
several meteorological variables simultaneously, and probably several others.
However we didn't agree on specific questions we want to answer, and probably
that should be a discussion for a future meeting.] 3.
Dependence measures for financial data. [Suggested by Jaya Vishwal.] 4. Time series models for non-normal data. [Suggested by Myron Katzoff. Motivated by epidemiology data, e.g. need for models for discrete data such as death counts. However it's also a problem that comes up with extreme values, e.g. data following a GPD when there is temporal dependence. I suggested looking at the paper by Davis, Dunsmuir and Streett (2003), Biometrika vol 90, 777-790. Perhaps we can use that paper as a springboard to a more general approach, including one that would allow for GEV or GPD as the marginal distribution.] |
References: [1] Stuart
G. Coles (1993), Regional Modelling of Extreme
Storms via Max-Stable Processes, JRSSB,
55, 797-816, [2] Stuart
G. Coles and Jonathan Tawn (1991), Modelling
Extreme Multivariate Events, JRSSB,
53, 377-392, pdf [3]
Stuart G. Coles and Jonathan Tawn (1994), Statistical
Methods for Multivariate Extremes: An Application to Structural Design, Applied Statistics, 43, 1-48, pdf [4] Stuart G. Coles and Jonathan Tawn
(1996), Modelling
of Extremes of the Areal Rainfall Process; JRSSB, 58, 329-347, pdf [5]
Beatriz Vaz de Melo Mendes and Luis Raul Pericchi,
Assessing Conditional Extremal Risk of Flooding
in [6] V.
Chavez-Demoulin and A. C. Davison (2005), Statistical
Methods for Multivariate Extremes: An Application
to Structural Design, Applied
Statistics, 54, 207-222, pdf [7] Janet E. Heffernan, Jonathan A.
Tawn and Zhengjun Zhang (2007), Asymptotically
(in)dependent multivariate maxima of moving maxima
processes, Extremes, 10, 57-82, pdf [8] Harry
Joe, Richard Smith and Ishay Weissman (1992),
Bivariate Threshold Methods for Extremes; JRSSB, 54, 171-183, pdf [9]
Anthony W. Ledford and Jonathan A. Tawn (2003), Diagnostics for dependence within time series extremes,
JRSSB, 65, 521-543, pdf [10]
Anthony W. Ledford and Jonathan A. Tawn (1996), Statistics for Nearly Extreme Values, Biometrika,83, 169-187,
pdf [11]
Anthony W. Ledford and Jonathan A. Tawn (1997), Modelling Dependence within Joint Tail Regions,JRSSB, 59, 475-499, ,pdf [12]
Krishanu Maulik and Sidney Resnick (2005), Characterizations
and Examples of Hidden Regular Variation,
Extremes, 7, 31-67, pdf [13]
Richard Smith (1994, Multivariate Threshold Methods, NIST/Temple University Conference on Extreme
Value Theory and its Applications, (Book Chapter) pdf
[14] Second
Order Regular Variation and Asymptotic [15]
Richard Smith, Jonathan Tawn and Stuart Coles (1997),
Markov Chain Models for Threshold Exceedances,
Biometrika, 84, 249-268, pdf [16] Alec
Stephenson, (2003) Simulating Multivariate Extreme
Value Distributions of Logistic Type, Extremes, 6, 49-59, pdf [17] Alec
Stephenson and Jonathan Tawn (2005) Exploiting
occurrence times in likelihood inference for componentwise
maxima, Biometrika, 92, 213-227, pdf [18] T.
Haising, C. Kluppelberg, G. Kuhn (2004) : Dependence estimation and
visualization in multivariate extremes with applications to financial data, Extremes 7 (2), 99-121, pdf Bayesian: [19] Behrens,
C., Lopes, H. and Gamerman, D. (2004) Bayesian analysis of extreme events with
threshold estimation, Statistical Modelling, 4, 227-244, pdf [20] Tancredi, A., Anderson, C. and Hagan, A. (2006) Accounting for threshold uncertainty in extreme value estimation, Extremes,
9, 87-106, pdf Preprints of Prof. Richard Smith: http://www.stat.unc.edu/postscript/rs/semstatrls.pdf(this is the paper I recommended as background reading for my tutorial last week)http://www.stat.unc.edu/postscript/rs/var.pdf(book chapter - about value at risk)http://www.stat.unc.edu/postscript/rs//insurance/inex.pdf(book chapter - my paper with Dougal Goodman)Bayesian approach to the insurance risk problem)http://www.stat.unc.edu/postscript/rs/extremal.pdf(Smith and Weissman 1996 - introduced M4 processes - unpublished)http://www.stat.unc.edu/postscript/rs/spatex.pdf(Smith 1991 - about max-stable processesunpublished)
SOME
DATA-SET Climate Data (suggested
by Kobi) http://iridl.ldeo.columbia.edu/index.html |
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Prof. Richard Smith gave a
tutorial on multivariate extreme value theory, sildes. |
Prof. Paul Schuette gave a
talk titled "Power laws and extreme values" in the application
working group, slides. |
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Prof. Dan Cooley gives an overview
about Spatial Extremes, sildes Prof. Pal Nabendu will give a
talk on estimation and testing with (univariate) EVD in the application
working group. The slides are here: [ 1 ] [ 2 ] [ 3 ] |
New
References: [21] Schlather, M. (2002) Models for
Stationary Max-Stable Random Fields.
Extremes, 5 (1), 33-44, pdf [22] Casson, E. and Coles, S. (1999)
Spatial Regression Models for Extremes, Extremes,
1 (4) 449-468. pdf [23] Davis, R. and Mikosch, T.
(2006) Extreme Value Theory for Space-time Processes with Heavy-tailed
Distributions, (forthcoming), pdf [24] Haan,
L.and Pereier, T. (2006) Spatial Extremes: Models for the Stationary Case, Annals of Statistics, 34, 146-168, pdf [25] Some
references from Dan Cooley homepage: http://www.stat.colostate.edu/~cooleyd/Papers/prediction.pdf http://www.stat.colostate.edu/~cooleyd/Papers/frRev.pdf http://www.stat.colostate.edu/~cooleyd/Papers/frAppendix.pdf [26]
Discussion paper: Weak and Strong Financial Frailty （2007） By J.L. Geluk, L. de Haan, and C. G. de Vries http://www.tinbergen.nl/discussionpapers/07023.pdf [27]
Zhang, Z. and Smith, R. (2007) On the Estimation and Application of
Max-Stable Processes http://www.stat.unc.edu/postscript/rs/zhangsmith07.pdf |
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Professor Jaya Bishwal will
talk on Financial Extremes. Abstract: First I will focus on Extremes of
Diffusion Models with special emphasis on Interest Rate Models, Stochastic
Volatility Models and Long Memory Models such as Superposition of
Ornstein-Uhlenbeck Models. Then I will talk on nonparametric estimation of
extreme dependence. Slides are available here |
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Meeting Cancelled because of NSF meeting |
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New
Reference: [28] Anne-Laure Fougeres, John Nolan
and Holger Rootzen (2007), Models for dependent extremes
using stable mixtures, pdf [29] Richard Davis, William Dunsmuir and Sarah Streett (2003), Observation-driven
models for Poisson counts, pdf [30] Maximum
Likelihood Estimation for an Observation Driven Model for Poisson Counts. Methodology
and Computing in Applied Probability 7, 149-159.pdf [31] |
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Vered Madar will talk about methods
for multiple comparisons and their possible application in extreme value
problems. slides |
Papers
about multiple comparisons (recommended by Vered) [32] Yoav Benjamini and Ruth Heller
(2006), False Discovery Rates for Spatial Signals, pdf [33] Yoav Benjamini1 and Daniel
Yekutieli2 (2001), THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE
TESTING UNDER DEPENDENCY, Annals of
Statistics, 29, 1165-1188, pdf [34] JOHN D. STOREY (2003), THE POSITIVE FALSE DISCOVERY RATE: A
BAYESIAN INTERPRETATION AND THE q-VALUE, Annals of Statistics, 6, 2013-2035. pdf [35] Bradley Efron, Local False Discovery Rates, pdf [36] Bradley Efron, Bayesians,
Frequentists and Scientists (2005), JASA,
100, 469, pdf [37] Yoav Benjamini and Yosef
Hochberg (1995), Controlling the False Discovery Rate: A Practical and
Powerful Approach to Multiple Testing. JRSS-B,
57, 289-300, pdf [38] Baruch Ziv, Hadas Saaroni, Anat
Baharad, Daniel Yekutieli, and Pinhas Alpert (2005), Indications for
aggravation in summer heat conditions over the Mediterranean Basin, GEOPHYSICAL RESEARCH LETTERS, 32, pdf [39] P. Alpert et al (2002), The
paradoxical increase of Mediterranean extreme daily rainfall in spite of
decrease in total values, GEOPHYSICAL
RESEARCH LETTERS, 29, pdf [40] E. L. Lehmann and Joseph P.
Romano (2005), GENERALIZATIONS OF THE FAMILYWISE ERROR RATE, Annals of Statistics, 33, 1138-1154, pdf [41] Bradley Efron et al (2001)Empirical Bayes Analysis of a Microarray
Experiment, JASA, 96, 1151-1160,
pdf |
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Thanks Giving, No meeting |
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Nicoleta Serban on high-dimensional wavelets and extremes, slides |
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12/06/07 |
Xiao Qin talk on Dependence Modelling in Multivariate Extremes, slides |
New References: [42] Philipp Hartmann, Stefan
Straetmans, Casper de Vries (2005),
Banking System Stability: A Cross-Atlantic Perspective, working paper, pdf [43] ALEXANDRA RAMOS and ANTHONY
LEDFORD (2005) Regular Score Tests of Independence in Multivariate Extreme
Values, Extremes 8, 5-26. pdf [44] TIM BEDFORD AND ROGER M. COOKE (2002), VINES-A NEW GRAPHICAL MODEL FOR
DEPENDENT RANDOM VARIABLES, Annals of
Statistics, 30, 1031-1068, pdf [45] Holger Rootzen and Nader Tajvidi, Multivariate
generalized Pareto distributions, pdf [46] Janet Hefferman (2000),
A Directory of Coefficients of Tail Dependence, Extremes 3, 279-290 pdf [47]
Gerrit Draisma, Holger Drees, Ana Ferreira, Laurens de Haan Bivariate tail
estimation: dependence in asymptotic independence, pdf [48] STUART
COLES, JANET HEFFERNAN, AND JONATHAN TAWN (1999) Dependence Measures for
Extreme Value Analyses, Extremes
2:4, 339-365, pdf [49] J. Beirlant, B. Vandewalle (2002), Some comments on the estimation of a dependence index in bivariate extreme value statistics, Statistics and Probability Letters, 60, 265-278, pdf |
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12/13/07 |
Richard Smith will talk about possibilities for extending the Ledford-Tawn
models to higher dimensions. slides |
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01/14/08 |
Overview of Davis, Dunsmuir and Streett (2003) Biometrika paper by Vangelis, slides |
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01/28/08 |
Laurens de Haan gives a talk about Extremal Processes |
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02/04/08 |
Round-Table
Discussions, pdf |
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02/11/08 |
Hurricane talk by Richard Smith, pdf |
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02/25/08 |
Sidney
Resnick’s slides |
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03/03/08 |
Alexandra
Ramos and Anthony Ledford’s slides |
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03/17/08 |
John
Nolan’s slides |
[50] Ilya
Molchanov (2007), Convex geometry of max-stable distributions, arxiv, pdf |
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03/31/08 |
Yimin
Xiao’ slides: An Introduction to Extreme
Value Theory of Gaussian Random Fields |
[51]
Keith Worsley (1996), The Geometry of Random Images, Chance, Vol 9, No1. pdf [52]
Reference List on Extreme Value Theory of Gaussian Random Fields, including
general theory, medical imaging and over-flow probability: pdf |
Group Members
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Name |
Affiliation |
Email Address |
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David Banks |
Duke University |
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Susie Bayarri |
University of Valencia and SAMSI |
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Jaya Bishwal |
UNC-Charlotte |
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Michela Cameletti |
SAMSI |
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Wei Chen |
SAS Institute |
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Guang Cheng |
Duke University |
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Dan Cooley |
Colorado State University |
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Sourish Das |
University of Connecticut |
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Dipak Dey |
University of Connecticut |
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Ian Dinwoodie |
Duke University |
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Evangelos Evangelou |
UNC-Chapel Hill |
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Elijah Gaioni |
University of Connecticut |
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Eric Gilleland |
NCAR |
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Dougal Goodman |
The Foundation for Science and Technology (UK) |
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Feng Guo |
University of Vermont |
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Jonathan Hill |
UNC-Chapel Hill |
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Jonathan Hosking |
IBM |
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Tailen Hsing |
University of Michigan |
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Rosalba Ignaccolo |
SAMSI |
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Huijing Jiang |
Georgia Institute of Technology |
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Myron Katzoff |
Centers for Disease Control |
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Yongku Kim |
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Lada Kyj |
Rice University |
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Anthony Ledford |
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Huitian Lu |
South Dakota State University |
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Wenbin Lu |
N.C. State University |
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Vered Madar |
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Pilar Munoz |
Technical University of Catalonia |
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XuanLong Nguyen |
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John Nolan |
American University |
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Jayanta Pal |
DUKE Univ. and SAMSI |
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Luis Pericchi |
University of Puerto Rico, Rio Piedras |
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Xiao Qin |
University of North Carolina, Chapel Hill |
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Cuirong Ren |
South Dakota State University |
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Abel Rodriguez |
Duke University |
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Holger Rootzen |
Chalmers University of Technology |
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Paul Schuette |
Meredith College |
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Nicoleta Serban |
Georgia Institute of Technology |