Related papers: A Matrix-Variate Log-Normal Model for Covariance M…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…

A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects…

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…

Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…

This work focuses on modeling of time-varying covariance matrices using the state covariance of linear stochastic systems. Following concepts from optimal mass transport and the Schr\"odinger bridge problem (SBP), we investigate several…

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…

This paper introduces a matrix-variate regression model for analyzing multivariate data observed across spatial locations and over time. The model's design incorporates a mean structure that links covariates to the response matrix and a…

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…

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…

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…

We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of…

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

We propose an approach to use the state covariance of linear systems to track time-varying covariance matrices of non-stationary time series. Following concepts from Riemmanian geometry, we investigate three types of covariance paths…

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…