In this paper we will prove a characterization for the independence of random vectors with positive (negative) orthant dependence according to a direction. The result can be seen as a generalization of a result by Lehmann [4].
We give a general definition of concordance and a set of axioms for measures of concordance. We then consider a family of measures satisfying these axioms. We compare our results with known results, in the discrete case.
Standard properties of -divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of -divergences, or the metricity of their powers. This paper extends the previously known family of -divergences with these properties. The extension consists of a continuum of -divergences which are squared metric distances and which are mostly new but include...
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.
The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.
Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.
This paper introduces a novel method for selecting a feature subset yielding an optimal trade-off between class separability and feature space dimensionality. We assume the following feature properties: (a) the features are ordered into a sequence, (b) robustness of the features decreases with an increasing order and (c) higher-order features supply more detailed information about the objects. We present a general algorithm how to find under those assumptions the optimal feature subset. Its performance...
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
The necessary and sufficient condition for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the expected mean in the general univariate linear regression model was given by Kruskal (1968) using a coordinate-free approach. The purpose of this article is to present in the same manner some alternative forms of this condition and to prove two of the Haberman’s equivalent conditions in a different and simpler way. The results obtained in the general univariate...