Related papers: Joint Covariance Estimation with Mutual Linear Str…
Covariance matrix estimation, a classical statistical topic, poses significant challenges when the sample size is comparable to or smaller than the number of features. In this paper, we frame covariance matrix estimation as a compound…
We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…
A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The…
In this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model…
Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Gaussian covariance graph model is a popular model in revealing underlying dependency structures among random variables. A Bayesian approach to the estimation of covariance structures uses priors that force zeros on some off-diagonal…
We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $\Sigma$ of…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
In this paper, we propose a novel framework for the joint identification of system dynamics and noise covariance in linear systems, under general noise distributions beyond Gaussian. Specifically, we would like to simultaneously estimate…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
We develop an envelope model for joint mean and covariance regression in the large $p$, small $n$ setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we…
Accurately modeling the correlation structure of errors is critical for reliable uncertainty quantification in probabilistic time series forecasting. While recent deep learning models for multivariate time series have developed efficient…
This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…
We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate,…
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…