Generalized Logistic Models and its orthant tail dependence

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009)

Distributions for one-lepton SUSY Searches with the ATLAS Detector

Using ATLAS data corresponding to 70 +- 8 nb^-1 of integrated luminosity from the 7 TeV proton-proton collisions at the LHC, distributions of relevant supersymmetry-sensitive variables are shown for the final state containing jets, missing transverse momentum and one isolated electron or muon. With increased integrated luminosities, selections based on these distributions will be used in the search for supersymmetric particles: it is thus important to show that the Standard Model backgrounds to these searches are under good control.Comment: 3 pages, to appear in the Proceedings of the Hadron Collider Physics Symposium 2010, Toronto, Ontario, Canada, 23 - 27 Aug 2010, available on the CERN document server under the number ATL-PHYS-PROC-2010-07

Rank-based inference for bivariate extreme-value copulas

Consider a continuous random pair $(X,Y)$ whose dependence is characterized by an extreme-value copula with Pickands dependence function $A$. When the marginal distributions of $X$ and $Y$ are known, several consistent estimators of $A$ are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859--878] and Cap\'{e}ra\`{a}, Foug\`{e}res and Genest [Biometrika 84 (1997) 567--577]. In this paper, rank-based versions of these estimators are proposed for the more common case where the margins of $X$ and $Y$ are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank-based estimators. Their finite- and large-sample performance is then compared to that of their known-margin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also given.Comment: Published in at http://dx.doi.org/10.1214/08-AOS672 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Conversation with Martin Bradbury Wilk

Martin Bradbury Wilk was born on December 18, 1922, in Montr\'{e}al, Qu\'{e}bec, Canada. He completed a B.Eng. degree in Chemical Engineering in 1945 at McGill University and worked as a Research Engineer on the Atomic Energy Project for the National Research Council of Canada from 1945 to 1950. He then went to Iowa State College, where he completed a M.Sc. and a Ph.D. degree in Statistics in 1953 and 1955, respectively. After a one-year post-doc with John Tukey, he became Assistant Director of the Statistical Techniques Research Group at Princeton University in 1956--1957, and then served as Professor and Director of Research in Statistics at Rutgers University from 1959 to 1963. In parallel, he also had a 14-year career at Bell Laboratories, Murray Hill, New Jersey. From 1956 to 1969, he was in turn Member of Technical Staff, Head of the Statistical Models and Methods Research Department, and Statistical Director in Management Sciences Research. He wrote a number of influential papers in statistical methodology during that period, notably testing procedures for normality (the Shapiro--Wilk statistic) and probability plotting techniques for multivariate data. In 1970, Martin moved into higher management levels of the American Telephone and Telegraph (AT&T) Company. He occupied various positions culminating as Assistant Vice-President and Director of Corporate Planning. In 1980, he returned to Canada and became the first professional statistician to serve as Chief Statistician. His accomplishments at Statistics Canada were numerous and contributed to a resurgence of the institution's international standing. He played a crucial role in the reinstatement of the Cabinet-cancelled 1986 Census.Comment: Published in at http://dx.doi.org/10.1214/08-STS272 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the covariance of the asymptotic empirical copula process

Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. Illustrations are provided and consequences for inference are outlined.Comment: 14 pages, 2 figure

Maty's Biography of Abraham De Moivre, Translated, Annotated and Augmented

November 27, 2004, marked the 250th anniversary of the death of Abraham De Moivre, best known in statistical circles for his famous large-sample approximation to the binomial distribution, whose generalization is now referred to as the Central Limit Theorem. De Moivre was one of the great pioneers of classical probability theory. He also made seminal contributions in analytic geometry, complex analysis and the theory of annuities. The first biography of De Moivre, on which almost all subsequent ones have since relied, was written in French by Matthew Maty. It was published in 1755 in the Journal britannique. The authors provide here, for the first time, a complete translation into English of Maty's biography of De Moivre. New material, much of it taken from modern sources, is given in footnotes, along with numerous annotations designed to provide additional clarity to Maty's biography for contemporary readers.Comment: Published at http://dx.doi.org/10.1214/088342306000000268 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The multivariate Hahn polynomials and the singular oscillator

Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated to the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect to the multidimensional hypergeometric distribution. The focus is put on the d=2 case for which the connection with the three-dimensional singular oscillator is used to derive the main properties of the polynomials: forward/backward shift operators, orthogonality relation, generating function, recurrence relations, bispectrality (difference equations) and explicit expression in terms of the univariate Hahn polynomials. The extension of these results to an arbitrary number of variables is presented at the end of the paper.Comment: 34 p

Goodness-of-fit Tests For Elliptical And Independent Copulas Through Projection Pursuit

Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets.Comment: 31 page