Related papers: Robust high-dimensional precision matrix estimatio…
Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…
In several applications, the underlying structure of the data allows for the samples to be organized into a matrix variate form. In such settings, the underlying row and column covariance matrices are fundamental quantities of interest. We…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…
We study the multivariate square-root lasso, a method for fitting the multivariate response linear regression model with dependent errors. This estimator minimizes the nuclear norm of the residual matrix plus a convex penalty. Unlike…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…
Sparse regression such as the Lasso has achieved great success in handling high-dimensional data. However, one of the biggest practical problems is that high-dimensional data often contain large amounts of missing values. Convex Conditioned…
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
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…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have…
Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…