Related papers: Bit Efficient Toeplitz Covariance Estimation

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…

This paper proposes a set of piecewise Toeplitz matrices as the linear mapping/sensing operator $\mathcal{A}: \mathbf{R}^{n_1 \times n_2} \rightarrow \mathbf{R}^M$ for recovering low rank matrices from few measurements. We prove that such…

This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…

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…

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance…

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…

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…

Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent sources in small uniform linear arrays, where ambiguities arise in…

Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

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…

Covariance matrices of noisy multichannel electroencephalogram time series data are hard to estimate due to high dimensionality. In brain-computer interfaces (BCI) based on event-related potentials and a linear discriminant analysis (LDA)…

We study operator-norm covariance estimation from heavy-tailed samples that may include a small fraction of arbitrary outliers. A simple and widely used safeguard is \emph{Euclidean norm clipping}, but its accuracy depends critically on an…

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…

This paper studies large $N$ and large $T$ conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the…

We present a general framework for using existing data to estimate the efficiency gain from using a covariate-adjusted estimator of a marginal treatment effect in a future randomized trial. We describe conditions under which it is possible…

Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition…

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…