Related papers: Robust Covariance and Scatter Matrix Estimation un…

This article introduces Huber means on Riemannian manifolds, providing a robust alternative to the Frechet mean by integrating elements of both square and absolute loss functions. The Huber means are designed to be highly resistant to…

As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…

A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…

As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the…

This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two…

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…

The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…

One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a…

We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…

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,…

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…

Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…

This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…

We address the problem of structured covariance matrix estimation for radar space-time adaptive processing (STAP). A priori knowledge of the interference environment has been exploited in many previous works to enable accurate estimators…

We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…

Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…