Related papers: Covariance matrix estimation in the singular case …

The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…

This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…

The modified Cholesky decomposition is popular for inverse covariance estimation, but often needs pre-specification on the full information of variable ordering. In this work, we propose a block Cholesky decomposition (BCD) for estimating…

A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…

Pocock and Simon's minimization method is a popular approach for covariate-adaptive randomization in clinical trials. Valid statistical inference with data collected under the minimization method requires the knowledge of the limiting…

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…

A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…

Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…

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…

This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…

This paper is concerned with optimizing the global minimum-variance portfolio's (GMVP) weights in high-dimensional settings where both observation and population dimensions grow at a bounded ratio. Optimizing the GMVP weights is highly…

The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance.…

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…

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…