Article
Statistics & Probability
Yangchang Xu, Ningning Xia
Summary: This paper investigates the limiting behavior of eigenvectors of the sample spatial sign covariance matrix (SSCM) by introducing the eigenvector empirical spectral distribution (VESD) with weights depending on the eigenvectors. The results show that the VESD of a large-dimensional sample SSCM converges to a generalized Marcenko-Pastur distribution when both the dimension p of observations and the sample size n tend to infinity proportionally. In addition, the central limit theorem of linear spectral statistics of VESD is established, implying that the eigenmatrix of sample SSCM and the classical sample covariance matrix are asymptotically the same.
JOURNAL OF MULTIVARIATE ANALYSIS
(2023)
Article
Physics, Fluids & Plasmas
W. Tarnowski, I. Yusipov, T. Laptyeva, S. Denisov, D. Chruscinski, K. Zyczkowski
Summary: By studying ensembles of quantum and classical random generators of N-dimensional Markovian evolution, we demonstrate the relationship between the two types of generators through superdecoherence. Increasing the strength of superdecoherence gradually leads to a sharp quantum-to-classical transition. Additionally, microscopic correlation between neighboring eigenvalues and the presence of horseshoe distribution, emblematic of the Ginibre universality class, is observed in both types of random generators even under superdecoherence and supercoherification.
Article
Business, Finance
Taras Bodnar, Nestor Parolya, Erik Thorsen
Summary: The main contribution of this paper is to derive the asymptotic behavior of the out-of-sample variance and out-of-sample relative loss, along with their empirical counterparts, in a high-dimensional setting. The results are obtained for different estimators of portfolio optimization. The paper highlights the limitations of using empirical out-of-sample variance and suggests using empirical out-of-sample relative loss as a more reliable measure in practice, particularly for portfolios with a large number of assets.
FINANCE RESEARCH LETTERS
(2023)
Article
Mathematics, Applied
David Hartman, Milan Hladik, David Riha
Summary: The study introduces an algorithm for computing the spectral decomposition of interval matrices and applies it to computing powers of interval matrices. By tight outer estimations of eigenvalues and eigenvectors, the algorithm achieves a total time complexity of O(n(4), discussing general interval matrices and symmetric interval matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Physics, Fluids & Plasmas
Wojciech Tarnowski
Summary: This paper investigates the properties of eigenvalues when randomness is introduced at the level of real matrix elements. It is found that in the limit of large matrix size, the density of real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line.
Article
Statistics & Probability
Jianqing Fan, Yingying Fan, Xiao Han, Jinchi Lv
Summary: This paper proposes a method called SIMPLE for statistical inference on membership profiles in large networks. It addresses the issue of quantifying the statistical uncertainty associated with the identification of latent links and provides methods for estimating unknown covariance matrices and the number of communities. The advantages and practical utility of the proposed method are demonstrated through simulation examples and real network applications.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2022)
Article
Engineering, Electrical & Electronic
Benjamin D. Robinson, Robert Malinas, Alfred O. Hero
Summary: This paper addresses the estimation of large interference covariance matrix in space-time adaptive detection, presenting a new estimator in the large dimensional limit which is proven to be ideal in detection theory. The performance of this estimator is compared through Monte Carlo simulations, showing higher detection probability than existing estimators.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Geochemistry & Geophysics
Ming Li, Guohao Sun, Jun Tong, Zishu He
Summary: This paper proposes a novel training sample selection method based on covariance matrix whitening, utilizing the RSCCM of the CUT as the TCM, whitening the subaperture's covariance matrix of the training sample, and deriving a criterion for selecting the training samples based on the maximum eigenvalue of the whitened subaperture's covariance matrix. The method shows improved stability and efficiency in selecting training samples compared to traditional methods.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2021)
Article
Statistics & Probability
Zhanting Long, Zeng Li, Ruitao Lin, Jiaxin Qiu
Summary: In this paper, we investigate the limiting behavior of the singular values of a lag-τ sample auto-correlation matrix Rετ in a high-dimensional factor model with vector white noise process. We establish the limiting spectral distribution (LSD) that characterizes the global spectrum of Rετ and derive the limit of its largest singular value. Under certain assumptions, we show that the LSD of Rετ is the same as the lag-τ sample auto-covariance matrix. Based on this equivalence, we propose two estimators of the total number of factors in a factor model using lag-τ sample auto-correlation matrices. The theoretical results are supported by numerical experiments.
JOURNAL OF MULTIVARIATE ANALYSIS
(2023)
Article
Mathematics
Pierluigi Benevieri, Alessandro Calamai, Massimo Furi, Maria Patrizia Pera
Summary: The study examines the persistence of eigenvalues and eigenvectors in perturbed eigenvalue problems in Hilbert spaces, assuming the unperturbed problem has a nontrivial kernel of odd dimension. A Rabinowitz-type global continuation result is proven using a topological approach based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.
Article
Engineering, Electrical & Electronic
Elias Raninen, David E. Tyler, Esa Ollila
Summary: This paper considers the problem of estimating high-dimensional covariance matrices of K-populations or classes when the sample sizes are comparable to the data dimension. It proposes a method to estimate each class covariance matrix as a linear combination of all class sample covariance matrices, which reduces the estimation error when the sample sizes are limited and the true class covariance matrices share a similar structure. The paper develops an effective method for estimating the coefficients in the linear combination and shows how the proposed method can be used for regularization parameter selection in a single class covariance matrix estimation problem. The proposed method is evaluated through numerical simulation studies and an application in global minimum variance portfolio optimization using real stock data.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Statistics & Probability
Cheng Liu, Moming Wang, Ningning Xia
Summary: In this paper, we introduce a new method for estimating integrated covariance matrices that uses a nonlinear shrinkage estimation strategy and denoising method, without requiring structure assumptions on the volatility matrix process. Our proposed estimator is asymptotically positive definite and demonstrates desirable estimation efficiency. Simulations and financial applications show that our estimator performs well compared to existing methods.
JOURNAL OF MULTIVARIATE ANALYSIS
(2022)
Article
Engineering, Electrical & Electronic
Taras Bodnar, Nestor Parolya, Erik Thorsen
Summary: In this paper, new results in random matrix theory are derived to construct a shrinkage estimator for the GMV portfolio with a random shrinkage target. The theory is applied to develop the dynamic estimation of the GMV portfolio, where the weights are shrunk to a holding portfolio. The paper considers both overlapping and non-overlapping samples and provides theoretical findings under weak assumptions on the data-generating process.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2023)
Article
Computer Science, Interdisciplinary Applications
Jing Zhou, Wei Lan, Hansheng Wang
Summary: This article proposes a novel method called Gaussian random perturbation for estimating the asymptotic covariance matrix of a general M-estimator. It avoids the need for derivative calculations and has the advantages of estimator consistency and parallel computing.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2022)
Article
Chemistry, Multidisciplinary
Fabio Rizzo, Chiara Bedon, Sulyman Mansour, Aleksander Pistol, Maria Francesca Sabba, Lukasz Flaga, Renata Klaput, Dora Foti
Summary: Flexible roofs are light and deformable, making them sensitive to wind actions and prone to local or global instability. Experimental wind tunnel testing is usually required to investigate the aerodynamic effects and structural response. However, the dynamic identification of the test model is challenging due to the reduced scale in wind tunnels. This paper explores the use of Singular Value Decomposition (SVD) to analyze ambient vibration accelerations of a scaled model and their spatial correlations for dynamic identification purposes.
APPLIED SCIENCES-BASEL
(2023)
Article
Engineering, Electrical & Electronic
David Gregoratti, Xavier Mestre
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2016)
Article
Engineering, Electrical & Electronic
Xavier Mestre, David Gregoratti
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2016)
Article
Computer Science, Information Systems
Xavier Mestre, Pascal Vallet
IEEE TRANSACTIONS ON INFORMATION THEORY
(2017)
Article
Engineering, Electrical & Electronic
Francois Rottenberg, Xavier Mestre, Dmitry Petrov, Francois Horlin, Jerome Louveaux
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2017)
Article
Engineering, Electrical & Electronic
Francois Rottenberg, Xavier Mestre, Francois Horlin, Jerome Louveaux
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2017)
Article
Computer Science, Information Systems
Guillem Femenias, Felip Riera-Palou, Xavier Mestre, Juan J. Olmos
Article
Engineering, Electrical & Electronic
Francois Rottenberg, Xavier Mestre, Francois Horlin, Jerome Louveaux
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2018)
Article
Engineering, Electrical & Electronic
Francois Rottenberg, Xavier Mestre, Francois Horlin, Jerome Louveaux
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2019)
Article
Engineering, Electrical & Electronic
Xavier Mestre, David Gregoratti, Peng Zhang
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS
(2020)
Article
Computer Science, Information Systems
David Gregoratti, Xavier Mestre, Xavier Vilajosana
IEEE WIRELESS COMMUNICATIONS LETTERS
(2020)
Article
Engineering, Electrical & Electronic
David Schenck, Xavier Mestre, Marius Pesavento
Summary: This article investigates the outlier production mechanism of the conventional MUSIC and g-MUSIC DoA estimation techniques using tools from Random Matrix Theory. A general Central Limit Theorem is derived to analyze the stochastic behavior of eigenvector-based cost functions in the asymptotic regime, and accurate predictions of the resolution capabilities of the methods are provided.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
A. Rosuel, P. Vallet, P. Loubaton, X. Mestre
Summary: This paper focuses on detecting useful signals in high-dimensional scenarios, proposing a new test based on SCM and evaluating its statistical performance through numerical simulations.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
David Schenck, Xavier Mestre, Marius Pesavento
Summary: In this article, the outlier production mechanism of the Partially Relaxed Deterministic Maximum Likelihood (PR-DML) Direction-of-Arrival estimator is investigated using tools from Random Matrix Theory. An accurate description of the probability of resolution for the PR-DML estimator is provided by analyzing the asymptotic behavior of the PR-DML cost function.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Xavier Mestre, Pascal Vallet
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2020)
Proceedings Paper
Engineering, Electrical & Electronic
Xavier Mestre, David Gregoratti, Peng (Peter) Zhang
2019 IEEE 20TH INTERNATIONAL WORKSHOP ON SIGNAL PROCESSING ADVANCES IN WIRELESS COMMUNICATIONS (SPAWC 2019)
(2019)