On measures of statistical dependence
On monotone dependence functions of the quantile type
We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
On simultaneous inference in multidimensional contingency tables
On Testing the Correlation Coefficient of a Bivariate Normal Distribution.
On the economic risk capital of portfolio insurance.
On the generation of correlation matrices.
On the measurement of stochastical dependence
On the significance level of the multirelation coefficient.
On the Variance, Reliability and Importance of Canonical Variables
Optimal solutions of multivariate coupling problems
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...
Orbital semilinear copulas
We introduce four families of semilinear copulas (i.e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital...
Original title unknown
Paramétrisation et analyse des correspondances
Pricing equity-indexed annuities under stochastic interest rates using copulas.
Quelques propriétés optimales en analyse des données, en termes de corrélation entre variables
Random noise and perturbation of copulas
For a random vector characterized by a copula we study its perturbation characterizing the random vector affected by a noise independent of both and . Several examples are added, including a new comprehensive parametric copula family .
Regularization for high-dimensional covariance matrix
In many applications, high-dimensional problem may occur often for various reasons, for example, when the number of variables under consideration is much bigger than the sample size, i.e., p >> n. For highdimensional data, the underlying structures of certain covariance matrix estimates are usually blurred due to substantial random noises, which is an obstacle to draw statistical inferences. In this paper, we propose a method to identify the underlying covariance structure by regularizing...
Robustness of the sample correlation -- the bivariate lognormal case.
Scatter halfspace depth: Geometric insights
Scatter halfspace depth is a statistical tool that allows one to quantify the fitness of a candidate covariance matrix with respect to the scatter structure of a probability distribution. The depth enables simultaneous robust estimation of location and scatter, and nonparametric inference on these. A handful of remarks on the definition and the properties of the scatter halfspace depth are provided. It is argued that the currently used notion of this depth is well suited especially for symmetric...
Scenario generation with distribution functions and correlations
In this paper, we present a method for generating scenarios for two-stage stochastic programs, using multivariate distributions specified by their marginal distributions and the correlation matrix. The margins are described by their cumulative distribution functions and we allow each margin to be of different type. We demonstrate the method on a model from stochastic service network design and show that it improves the stability of the scenario-generation process, compared to both sampling and a...