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The problems of uniform linear array (with uniform mutual coupling) calibration and Toeplitz covariance matrix estimation are re-examined for application in the receive arrays of modern High Frequency Over-the-Horizon Radars (HF OTHR).…

Signal Processing · Electrical Eng. & Systems 2024-09-20 Yuri Abramovich , Tanit Pongsiri

The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix…

Optimization and Control · Mathematics 2012-08-31 Anders Lindquist , Giorgio Picci

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

Signal Processing · Electrical Eng. & Systems 2021-10-26 Augusto Aubry , Prabhu Babu , Antonio De Maio , Rikhabchand Jyothi

We address structured covariance estimation in elliptical distributions by assuming that the covariance is a priori known to belong to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of…

Machine Learning · Statistics 2023-07-19 Ilya Soloveychik , Ami Wiesel

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

Signal Processing · Electrical Eng. & Systems 2025-05-13 Augusto Aubry , Prabhu Babu , Antonio De Maio , Massimo Rosamilia

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…

Information Theory · Computer Science 2019-03-19 Wei Cui , Xu Zhang , Yulong Liu

The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but…

Signal Processing · Electrical Eng. & Systems 2021-06-08 Kaushallya Adhikari

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…

Data Structures and Algorithms · Computer Science 2025-04-15 Gleb Novikov

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Methodology · Statistics 2025-12-30 Shaoxin Wang , Ziyun Ma

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Machine Learning · Statistics 2013-06-19 Ilya Soloveychik , Ami Wiesel

This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…

Numerical Analysis · Computer Science 2014-11-04 Mostafa Rahmani , George Atia

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…

Machine Learning · Statistics 2017-05-01 Farhad Pourkamali-Anaraki

We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying…

Dynamical Systems · Mathematics 2026-02-11 Vladimir R. Kostic , Karim Lounici , Massimiliano Pontil

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…

Statistics Theory · Mathematics 2024-05-09 Piotr Zwiernik

An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…

Numerical Analysis · Mathematics 2025-10-20 Denis Grishin , Thomas Strohmer

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Machine Learning · Statistics 2016-06-03 Jinghui Chen , Quanquan Gu

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…

Statistics Theory · Mathematics 2017-06-13 Mengjie Chen , Chao Gao , Zhao Ren

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

Machine Learning · Statistics 2019-01-16 Martin Azizyan , Akshay Krishnamurthy , Aarti Singh

We observe $n$ independent $p-$dimensional Gaussian vectors with missing coordinates, that is each value (which is assumed standardized) is observed with probability $a>0$. We investigate the problem of minimax nonparametric testing that…

Statistics Theory · Mathematics 2016-02-16 Cristina Butucea , Rania Zgheib

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani