On multiple normal probabilities of rectangles
On one multivariate linear model with nuisance parameters
On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions
On optimality of the LR tests in the sense of exact slopes. I. General case
On orderings induced by the Loewner partial ordering
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.
On probabilities in certain multivariate distributions: their dependence on correlations
On quasi-homogeneous copulas
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.
On Seifert's ANOVA-like test for variance components
On selecting the best features in a noisy environment
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...
On simultaneous inference in multidimensional contingency tables
On solution sets of information inequalities
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.
On some alternative forms equivalent to Kruskal's condition for OLSE to be BLUE.
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...
On structural approximating multivariate discrete probability distributions
On testing hypotheses approximable by cones
On Testing the Correlation Coefficient of a Bivariate Normal Distribution.
On Testing the Dimensionality of Regression Coefficients.
On the admissibility of tests for discrete exponential families
On the asymptotic distributions of certain functional of eigenvalues of correlation matrices
On the Bayes approach in general multiple autoregressive series
On the Bayesian estimation for the stationary Neyman-Scott point processes
The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good as the fast...