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Related papers: Robust spiked random matrices and a robust G-MUSIC…

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We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…

Statistics Theory · Mathematics 2023-01-18 Ji Hyung Jung , Hye Won Chung , Ji Oon Lee

Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…

Statistics Theory · Mathematics 2017-06-13 Mengjie Chen , Chao Gao , Zhao Ren

In this paper, we study the MUltiple SIgnal Classification (MUSIC) algorithm often used to image small targets when multiple measurement vectors are available. We show that this algorithm may be used when the imaging problem can be cast as…

Numerical Analysis · Mathematics 2019-01-23 Miguel Moscoso , Alexei Novikov , George Papanicolaou , Chrysoula Tsogka

G-computation has become a widely used robust method for estimating unconditional (marginal) treatment effects with covariate adjustment in the analysis of randomized clinical trials. Statistical inference in this context typically relies…

Methodology · Statistics 2025-03-18 Xin Zhang , Haitao Chu , Lin Liu , Satrajit Roychoudhury

The problem of estimating a spiked covariance matrix in high dimensions under Frobenius loss, and the parallel problem of estimating the noise in spiked PCA is investigated. We propose an estimator of the noise parameter by minimizing an…

Statistics Theory · Mathematics 2014-08-28 Didier Chételat , Martin T. Wells

We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…

Data Structures and Algorithms · Computer Science 2022-02-22 Jingqiu Ding , Samuel B. Hopkins , David Steurer

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…

Applications · Statistics 2019-11-20 Andrea Cappozzo , Francesca Greselin , Thomas Brendan Murphy

This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window…

Probability · Mathematics 2012-08-22 Walid Hachem , Philippe Loubaton , X. Mestre , Jamal Najim , Pascal Vallet

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

Probability · Mathematics 2015-01-20 Romain Couillet , Matthew R. McKay

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

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…

Statistics Theory · Mathematics 2020-09-04 Zhigang Bao , Xiucai Ding , Jingming Wang , Ke Wang

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

Statistics Theory · Mathematics 2020-09-25 Zhixiang Zhang , Shurong Zheng , Guangming Pan , Pingshou Zhong

In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone's spiked covariance…

Probability · Mathematics 2020-01-01 Xiucai Ding

The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double precision…

High Energy Physics - Phenomenology · Physics 2024-10-04 Enrico Bothmann , John M. Campbell , Stefan Höche , Max Knobbe

Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…

Statistics Theory · Mathematics 2024-01-23 Zeqin Lin , Guangming Pan , Peng Zhao , Jia Zhou

The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…

Machine Learning · Statistics 2025-09-08 Gautam Kamath

Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…

Numerical Analysis · Mathematics 2026-05-18 Caroline Wormell

In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…

Methodology · Statistics 2026-03-31 Mengxi Yi , David Tyler

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are…

Econometrics · Economics 2024-05-29 Shakeeb Khan , Tatiana Komarova , Denis Nekipelov

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

Statistics Theory · Mathematics 2025-02-17 Hao Yan , Keith Levin