Related papers: Maximal Invariants For Lorentz Wishart Models

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with…

We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…

We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F =…

Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…

This paper proposes improved methods for the maximum likelihood (ML) estimation of the equivalent number of looks $L$. This parameter has a meaningful interpretation in the context of polarimetric synthetic aperture radar (PolSAR) images.…

This paper develops on-line inference for the multivariate local level model, with the focus being placed on covariance estimation of the innovations. We assess the application of the inverse Wishart prior distribution in this context and…

This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…

We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…

This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…

We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can…

To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…

The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in [Vila et al., 2022, Bivariate Log-symmetric Models: Theoretical Properties and Parameter Estimation. Avaliable at…

We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…