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The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…

Methodology · Statistics 2021-09-15 Jiaxin Qiu , Zeng Li , Jianfeng Yao

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

Signal Processing · Electrical Eng. & Systems 2025-05-22 Lennard Rompelberg , Michael T. Schaub

A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…

Methodology · Statistics 2024-08-27 Stef Baas , Richard J. Boucherie , Jean-Paul Fox

We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate…

Statistics Theory · Mathematics 2020-11-26 Kwangmin Lee , Kyoungjae Lee , Jaeyong Lee

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

Methodology · Statistics 2021-05-17 Peng Tang , Huijing Jiang , Heeyoung Kim , Xinwei Deng

Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…

Methodology · Statistics 2025-03-07 Shiva Kaul , Min-Gyu Kim

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…

Methodology · Statistics 2008-02-04 K. Triantafyllopoulos

Consider $n$ independent and identically distributed $p$-dimensional Gaussian random vectors with covariance matrix $\Sigma.$ The problem of estimating $\Sigma$ when $p$ is much larger than $n$ has received a lot of attention in recent…

Statistics Theory · Mathematics 2016-03-07 Danning Li , Hui Zou

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

Methodology · Statistics 2011-02-14 Tony Cai , Weidong Liu , Xi Luo

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

Information Theory · Computer Science 2011-01-21 Alexander Jung , Sebastian Schmutzhard , Franz Hlawatsch , Alfred O. Hero

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…

Information Theory · Computer Science 2015-06-03 Jianfeng Yao , Abla Kammoun , Jamal Najim

We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure…

Machine Learning · Computer Science 2026-01-28 Emily C. Ehrhardt , Felipe Tobar

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

Statistics Theory · Mathematics 2008-06-26 Adam J. Rothman , Peter J. Bickel , Elizaveta Levina , Ji Zhu

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by…

Econometrics · Economics 2026-01-26 Kim Christensen , Mark Podolskij , Nopporn Thamrongrat , Bezirgen Veliyev

Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…

Statistics Theory · Mathematics 2024-10-23 Lior Horesh , Vasileios Kalantzis , Yingdong Lu , Tomasz Nowicki

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

Machine Learning · Statistics 2025-05-13 Samuel Erickson , Tobias Rydén

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

Machine Learning · Computer Science 2020-10-20 Di Wang , Xiangyu Guo , Chaowen Guan , Shi Li , Jinhui Xu

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

Methodology · Statistics 2019-03-12 Yuan Ke , Stanislav Minsker , Zhao Ren , Qiang Sun , Wen-Xin Zhou