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Related papers: M-Functionals of Multivariate Scatter

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Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

Methodology · Statistics 2025-11-21 Soumya Chakraborty , Ayanendranath Basu , Abhik Ghosh

This paper proposes an original approach to better understanding the behavior of robust scatter matrix $M$-estimators. Scatter matrices are of particular interest for many signal processing applications since the resulting performance…

Methodology · Statistics 2018-11-07 Gordana Draskovic , Frederic Pascal

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

Instrumentation and Detectors · Physics 2024-03-13 Elise Colin , Razvigor Ossikovski

This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…

Applications · Statistics 2016-06-29 Ying Sun , Prabhu Babu , Daniel P. Palomar

The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…

Methodology · Statistics 2020-07-10 Ghulam A. Qadir , Ying Sun

We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed…

Methodology · Statistics 2023-05-09 Esa Ollila , Daniel P. Palomar , Frederic Pascal

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…

Statistics Theory · Mathematics 2022-08-23 Timothée Mathieu

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…

Statistics Theory · Mathematics 2020-08-04 John Goes , Gilad Lerman , Boaz Nadler

We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…

Methodology · Statistics 2023-10-17 Rahul Ghosal , Marcos Matabuena

This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional…

Statistics Theory · Mathematics 2025-11-17 Axel Bücher , Johan Segers , Torben Staud

In many problems from multivariate analysis, the parameter of interest is a shape matrix, that is, a normalized version of the corresponding scatter or dispersion matrix. In this paper, we propose a depth concept for shape matrices that…

Statistics Theory · Mathematics 2018-12-03 Davy Paindaveine , Germain Van Bever

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

Dynamical Systems · Mathematics 2023-11-03 A. Vershik

In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…

Statistics Theory · Mathematics 2013-09-20 David Källberg , Oleg Seleznjev

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

Statistics Theory · Mathematics 2024-11-08 Natalie Neumeyer , Leonie Selk

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Machine Learning · Statistics 2013-01-16 Hachem Kadri , Philippe Preux , Emmanuel Duflos , Stéphane Canu

In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…

Applications · Statistics 2015-09-30 Ilya Soloveychik , Dmitry Trushin , Ami Wiesel

In this article, we establish a test for multivariate scatter parameter in elliptical model, where the location parameter is known, and the scatter parameter is estimated by the multivariate forward search method. The consistency property…

Methodology · Statistics 2018-11-27 Chitradipa Chakraborty

Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…

Methodology · Statistics 2023-01-11 Weijuan Liang , Qingzhao Zhang , Shuangge Ma

We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…

Functional Analysis · Mathematics 2025-10-27 Jiajia Ding , Jasson Vindas , Yunyun Yang

In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all…

Probability · Mathematics 2018-10-17 Dustin Kremer , Hans-Peter Scheffler