Related papers: Robust $M$-Estimation of Scatter Matrices via Prec…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…
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…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…
The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
This paper proposes a quasi-maximum likelihood (QML) estimator for break points in high-dimensional factor models, specifically accounting for multiple structural breaks. We begin by establishing a necessary and sufficient condition to…
We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…
Recently, we have proposed a maximum likelihood iterative algorithm for estimation of the parameters of the Nakagami-m distribution. This technique performs better than state of art estimation techniques for this distribution. This could be…
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…
We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…
The determination of the covariance matrix and its inverse, the precision matrix, is critical in the statistical analysis of cosmological measurements. The covariance matrix is typically estimated with a limited number of simulations at…
We introduce the dispersion models with a regression structure to extend the generalized linear models, the exponential family nonlinear models (Cordeiro and Paula, 1989) and the proper dispersion models (J{\o}rgensen, 1997a). We provide a…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…