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1
Content available remote

Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology

100%
Dutfoy A., Parey S., Roche N.
Dependence Modeling
|
2014
|
tom 2
|
nr 1
EN
In this paper, we provide a tutorial on multivariate extreme value methods which allows to estimate the risk associated with rare events occurring jointly. We draw particular attention to issues related to extremal dependence and we insist on the asymptotic independence feature. We apply the multivariate extreme value theory on two data sets related to hydrology and meteorology: first, the joint flooding of two rivers, which puts at risk the facilities lying downstream the confluence; then the joint occurrence of high speed wind and low air temperatures, which might affect overhead lines.
2
Content available remote

Inference for copula modeling of discrete data: a cautionary tale and some facts

100%
Faugeras O. P.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
121-132
EN
In this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.
3
Content available remote

On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

84%
Di Bernardino E., Rullière D.
Dependence Modeling
|
2013
|
tom 1
1-36
EN
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.
4
Content available remote

New copulas based on general partitions-of-unity and their applications to risk management (part II)

84%
Pfeifer D., Mändle A., Ragulina O.
Dependence Modeling
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2017
|
tom 5
|
nr 1
246-255
EN
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.
5
Content available remote

Matrix rank and inertia formulas in the analysis of general linear models

84%
Tian Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
126-150
EN
Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias of covariances of predictors and estimators of parameter spaces in general linear models (GLMs), and how to use the formulas in statistical analysis of GLMs. We first derive analytical expressions of best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameters in the model by solving a constrained quadratic matrix-valued function optimization problem, and present some well-known results on ordinary least-squares predictors/ordinary least-squares estimators (OLSPs/OLSEs). We then establish some fundamental rank and inertia formulas for covariance matrices related to BLUPs/BLUEs and OLSPs/OLSEs, and use the formulas to characterize a variety of equalities and inequalities for covariance matrices of BLUPs/BLUEs and OLSPs/OLSEs. As applications, we use these equalities and inequalities in the comparison of the covariance matrices of BLUPs/BLUEs and OLSPs/OLSEs. The work on the formulations of BLUPs/BLUEs and OLSPs/OLSEs, and their covariance matrices under GLMs provides direct access, as a standard example, to a very simple algebraic treatment of predictors and estimators in linear regression analysis, which leads a deep insight into the linear nature of GLMs and gives an efficient way of summarizing the results.
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