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Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…

Statistics Theory · Mathematics 2013-12-09 Johanna Hardin , Stephan Ramon Garcia , David Golan

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp…

Statistics Theory · Mathematics 2017-05-30 Fang Han , Sheng Xu , Wen-Xin Zhou

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…

Econometrics · Economics 2024-04-02 Jacob Schwartz , Kyungchul Song

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

Methodology · Statistics 2025-10-07 Thomas Muschinski , Georg J. Mayr , Thorsten Simon , Nikolaus Umlauf , Achim Zeileis

We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…

Information Theory · Computer Science 2020-01-27 Jean Barbier

The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…

Methodology · Statistics 2016-11-29 Haeran Cho , Piotr Fryzlewicz

This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…

Econometrics · Economics 2025-02-13 Jiti Gao , Fei Liu , Bin Peng , Yayi Yan

We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the…

Computation · Statistics 2024-05-14 Sean Pinkney

The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$…

Computation · Statistics 2018-11-13 Ofer Shwartz , Boaz Nadler

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…

Statistics Theory · Mathematics 2023-12-25 Qianqian Jiang , Jiaxin Qiu , Zeng Li

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…

Data Analysis, Statistics and Probability · Physics 2024-09-19 Daniel Nagel , Georg Diez , Gerhard Stock

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…

Statistical Mechanics · Physics 2007-05-23 W. Pietsch

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…

Econometrics · Economics 2025-03-10 Denis Kojevnikov , Vadim Marmer , Kyungchul Song

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…

Statistics Theory · Mathematics 2015-04-15 Ery Arias-Castro , Sébastien Bubeck , Gábor Lugosi

We study sample covariance matrices arising from multi-level components of variance. Thus, let $ B_n=\frac{1}{N}\sum_{j=1}^NT_{j}^{1/2}x_jx_j^TT_{j}^{1/2}$, where $x_j\in R^n$ are i.i.d. standard Gaussian, and…

Probability · Mathematics 2024-06-07 Ran Xie , Iain Johnstone

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…

Statistics Theory · Mathematics 2018-03-22 Jiang Hu , Weiming Li , Zhi Liu , Wang Zhou

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

Methodology · Statistics 2026-05-15 Wenhao Zhang , Zhaoxing Gao

This paper studies the central limit theorems (CLTs) for linear spectral statistics (LSSs) of general sample covariance matrices, when the test functions belong to $C^3$, the class of functions with continuous third order derivatives. We…

Statistics Theory · Mathematics 2026-03-16 Jian Cui , Zhijun Liu , Jiang Hu , Zhidong Bai

This article is concerned with the spectral behavior of $p$-dimensional linear processes in the moderately high-dimensional case when both dimensionality $p$ and sample size $n$ tend to infinity so that $p/n\to0$. It is shown that, under an…

Statistics Theory · Mathematics 2015-04-27 Lili Wang , Alexander Aue , Debashis Paul

Under the Kolmogorov--Smirnov metric, an upper bound on the rate of convergence to the Gaussian distribution is obtained for linear statistics of the matrix ensembles in the case of the Gaussian, Laguerre, and Jacobi weights. The main lemma…

Probability · Mathematics 2020-06-16 Sergey Berezin , Alexander I. Bufetov