Related papers: High-Performance Variance-Covariance Matrix Constr…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-based inference with a very small sample size. However, in…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of…
Let $\mathcal{P}_{2,ac}$ be the set of Borel probabilities on $\mathbb{R}^d$ with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fr\'echet mean) of a…
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective…
A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
In observational causal inference, in order to emulate a randomized experiment, weights are used to render treatments independent of observed covariates. This property is known as balance; in its absence, estimated causal effects may be…
The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares…