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Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…

Probability · Mathematics 2012-06-14 Richard Y. Chen , Alex Gittens , Joel A. Tropp

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 present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…

Statistics Theory · Mathematics 2024-03-27 Roberto I. Oliveira , Zoraida F. Rico

We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix…

Probability · Mathematics 2021-08-21 Kevin Schnelli , Yuanyuan Xu

This article is due to appear in the Handbook of Statistics, Vol. 43, Elsevier/North-Holland, Amsterdam, edited by Arni S. R. Srinivasa Rao and C. R. Rao. In modern day analytics, there is ever growing need to develop statistical models to…

Statistics Theory · Mathematics 2019-08-20 Deepak Nag Ayyala

We consider estimation of high-dimensional long-run covariance matrices for time series with nonconstant means, a setting in which conventional estimators can be severely biased. To address this difficulty, we propose a difference-based…

Methodology · Statistics 2026-03-19 Yanhong Liu , Fengyi Song , Long Feng

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…

Numerical Analysis · Mathematics 2021-05-11 Mostafa Ghadampour , Donal O'Regan , Ebrahim Soori , Ravi. p. Agarwal

We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain…

Statistics Theory · Mathematics 2010-01-05 Noureddine El Karoui

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

Econometrics · Economics 2019-10-29 Jaeheon Jung

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

Statistics Theory · Mathematics 2014-06-23 Damien Passemier , Zhaoyuan Li , Jian-Feng Yao

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…

Probability · Mathematics 2012-05-31 Olga Friesen , Matthias Löwe

Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.

Statistics Theory · Mathematics 2019-09-13 Niushan Gao , Alexandra Kirillova , Zihao Tong

High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…

Methodology · Statistics 2021-04-28 Jinyuan Chang , Song Xi Chen , Cheng Yong Tang , Tong Tong Wu

The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…

Probability · Mathematics 2015-11-10 Vladislav Kargin

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…

Statistics Theory · Mathematics 2017-03-03 Alexandre Belloni , Victor Chernozhukov , Abhishek Kaul

We use statistical mechanics techniques, viz. the replica method, to model the effect of censoring on overfitting in Cox's proportional hazards model, the dominant regression method for time-to-event data. In the overfitting regime, Maximum…

Methodology · Statistics 2023-12-06 Emanuele Massa , Alexander Mozeika , Anthony Coolen

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…

Methodology · Statistics 2015-04-17 Jianqing Fan , Yuan Liao , Han Liu

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

We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…

Statistics Theory · Mathematics 2015-03-13 Mengyu Xu , Danna Zhang , Wei Biao Wu

Sampling from multiple distributions so as to maximize overlap has been studied by statisticians since the 1950s. Since the 2000s, such correlated sampling from the probability simplex has been a powerful building block in disparate areas…

Data Structures and Algorithms · Computer Science 2025-11-18 Joseph , Naor , Nitya Raju , Abhishek Shetty , Aravind Srinivasan , Renata Valieva , David Wajc