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In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…

Statistics Theory · Mathematics 2022-05-17 Saulius Jokubaitis , Remigijus Leipus

A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices $X=\sum_i g_i A_i$ where $g_i$ are independent…

Probability · Mathematics 2023-09-18 Afonso S. Bandeira , March T. Boedihardjo , Ramon van Handel

It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n$\in$Z with independent components satisfy at each…

Statistics Theory · Mathematics 2025-11-19 Philippe Loubaton , Alexis Rosuel , Pascal Vallet

This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the…

Mathematical Physics · Physics 2023-07-07 G. Borot , A. Guionnet , K. K. Kozlowski

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

Statistics Theory · Mathematics 2025-01-17 Cristina Butucea , Alexander Meister , Angelika Rohde

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf…

Probability · Mathematics 2012-01-04 Z. D. Bai , H. X. Liu , W. K. Wong

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

Statistics Theory · Mathematics 2026-01-28 Annika Betken , Herold Dehling

In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…

Statistics Theory · Mathematics 2011-06-22 Markus Bibinger

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…

Information Theory · Computer Science 2019-03-11 Guanping Lu , Jinsong Wu , Robert C. Qiu

We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression…

Probability · Mathematics 2016-03-01 Kamil Jurczak , Angelika Rohde

We study the asymptotic properties of the GLS estimator in multivariate regression with heteroskedastic and autocorrelated errors. We derive Wald statistics for linear restrictions and assess their performance. The statistics remains robust…

Econometrics · Economics 2025-03-19 Koichiro Moriya , Akihiko Noda

This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…

Statistics Theory · Mathematics 2024-04-24 Xiucai Ding , Yun Li , Fan Yang

We study a class of Hermitian random matrices which includes and generalizes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN random…

Probability · Mathematics 2016-02-16 Paul Jung

In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large $N$, of the logarithm of the partition function of $N \times N$ Hermitian random matrices. These…

Mathematical Physics · Physics 2007-05-23 N. M. Ercolani , K. D. T-R McLaughlin , V. U. Pierce

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

Probability · Mathematics 2024-11-14 Manjunath Krishnapur , D. Yogeshwaran

We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time.…

Statistics Theory · Mathematics 2020-01-16 Johannes Heiny , Thomas Mikosch

In this paper, we consider directly estimating the eigenvalues of precision matrix, without inverting the corresponding estimator for the eigenvalues of covariance matrix. We focus on a general asymptotic regime, i.e., the large dimensional…

Statistics Theory · Mathematics 2025-09-22 Jie Zhou , Junhao Xie , Jiaqi Chen

This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p…

Statistics Theory · Mathematics 2026-04-30 Wonjun Seo

An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…

Statistical Mechanics · Physics 2017-09-25 Aurélien Grabsch , Christophe Texier

Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…

Applications · Statistics 2018-02-13 Zenan Ling , Robert C. Qiu , Xing He , Lei Chu