相关论文: On Elliptical and Inverse Elliptical Wishart distr…
Let $X^{(\delta)}$ be a Wishart process of dimension $\delta$, with values in the set of positive matrices of size $m$. We are interested in the large deviations for a family of matrix-valued processes $\{\delta^{-1} X_t^{(\delta)}, t \leq…
Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \times p$ random matrix with…
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments.…
These lecture notes provide an introduction to the theory of Wishart distributions and Wishart processes, particularly what concerns their existence and their realizations as solutions of Wishart SDEs. The material is based on recent…
Chance constraints describe a set of given random inequalities depending on the decision vector satisfied with a large enough probability. They are widely used in decision making under uncertain data in many engineering problems. This paper…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, poses serious challenges for analytical calculations. Often…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…
Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…
The normal-inverse-Wishart (NIW) distribution is commonly used as a prior distribution for the mean and covariance parameters of a multivariate normal distribution. The family of NIW distributions is also a minimal exponential family. In…
This paper describes the Elliptical Quartic Exponential distribution in $\mathbb{R}^D$, obtained via a maximum entropy construction by imposing second and fourth moment constraints. I discuss relationships to related work, analytical…
Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…
We establish an identity for E f (Y) -E f (X), when X and Y both have matrix variateskew-normal distributions and the function f fulfills some weak conditions. Thecharacteristic function of matrix variate skew normal distribution is then…
We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of…