Reflection coefficients vs partial autocorrelations.
Remarks on Two Product-like Constructions for Copulas
We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the -product and the -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
Rolling-ball method for estimating the boundary of the support of a point-process intensity
Semigroups of Semi-copulas and Evolution of Dependence at Increase of Age.
Shuffles of Min.
Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which...
Sobre la representación de un conjunto mediante árboles aditivos.
En este trabajo se estudia el problema de la representación de un conjunto mediante árboles aditivos, en el sentido de hallar una formalización que permita abordar el mismo desde la perspectiva general de los métodos geométricos de representación del análisis multivariante.
Solution to an open problem about a transformation on the space of copulas
We solve a recent open problem about a new transformation mapping the set of copulas into itself. The obtained mapping is characterized in algebraic terms and some limit results are proved.
Some Characterizations of the Bivariate Normal Distribution.
Some functionals for copulas.
Some New Random Effect Models for Correlated Binary Responses
Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity...
Statistical aspects of associativity for copulas
In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity...
Statistiques de diffusions et temps local
Sur les lois à symétrie elliptique
Symmetries of random discrete copulas
In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
The determination of factors in linear models of factor analysis
The author shows that a decomposition of a covariance matrix implies the corresponding model, i.e. the existence of factors such that is true. The result is applied to the general linear model of factor analysis. A procedure for computing the factor score is proposed.
The generalized FGM distribution and its application to stereology of extremes
The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.
The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.
The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"
The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason...
The role of functional equations in stochastic model building.
The use of copulas in the study of certain transforms of random variables with applications in finance.