Related papers: Robust and Resistant Regularized Covariance Matric…

This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…

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…

Robust estimators for generalized linear models (GLMs) are not easy to develop due to the nature of the distributions involved. Recently, there has been growing interest in robust estimation methods, particularly in contexts involving a…

We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…

We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters…

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…

This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…

Let $X$ be a centered random vector taking values in $\mathbb{R}^d$ and let $\Sigma= \mathbb{E}(X\otimes X)$ be its covariance matrix. We show that if $X$ satisfies an $L_4-L_2$ norm equivalence, there is a covariance estimator…

This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266,…

Grouping observations into homogeneous groups is a recurrent task in statistical data analysis. We consider Gaussian Mixture Models, which are the most famous parametric model-based clustering method. We propose a new robust approach for…

Multi-source stationary computed tomography (MSS-CT) offers significant advantages in medical and industrial applications due to its gantry-less scan architecture and/or capability of simultaneous multi-source emission. However, the lack of…

The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error…

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…

The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…