English
Related papers

Related papers: Notes on asymptotics of sample eigenstructure for …

200 papers

The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample…

Statistics Theory · Mathematics 2013-03-26 Dan Shen , Haipeng Shen , Hongtu Zhu , J. S. Marron

The present manuscript studies signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked…

Statistics Theory · Mathematics 2018-04-03 Debapratim Banerjee , Zongming Ma

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…

Statistics Theory · Mathematics 2023-11-21 Long Yu , Peng Zhao , Wang Zhou

Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications. To this end, in this paper we introduce a general…

Statistics Theory · Mathematics 2020-10-14 Jianqing Fan , Yingying Fan , Xiao Han , Jinchi Lv

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

Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show…

Statistics Theory · Mathematics 2026-03-16 Daniel G. Rasines , G. Alastair Young

In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance…

Probability · Mathematics 2013-07-08 Qinwen Wang , Jack W. Silverstein , Jianfeng Yao

We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…

Mathematical Physics · Physics 2015-05-13 Delphine Féral , Sandrine Péché

The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…

Statistics Theory · Mathematics 2015-03-19 Han Xiao , Wei Biao Wu

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…

Statistics Theory · Mathematics 2016-12-20 Lihua Lei , Peter J. Bickel , Noureddine El Karoui

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Statistics Theory · Mathematics 2012-11-26 Stefano Favaro , Antonio Lijoi , Igor Prünster

If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…

Econometrics · Economics 2018-08-06 Laurent Davezies , Xavier D'Haultfoeuille , Yannick Guyonvarch

In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity…

Information Theory · Computer Science 2012-06-20 Romain Couillet , Walid Hachem

In the spiked population model introduced by Johnstone (2001),the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation…

Statistics Theory · Mathematics 2012-06-06 Zhidong Bai , Jian-Feng Yao

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

Statistics Theory · Mathematics 2024-05-16 Lucas Reding , Andrés F. López-Lopera , François Bachoc

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…

Statistics Theory · Mathematics 2024-09-25 Claudia Kirch , Alexander Meier , Renate Meyer , Yifu Tang

Although complete randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards…

Statistics Theory · Mathematics 2017-08-15 Xinran Li , Peng Ding , Donald B. Rubin

This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic…

Statistics Theory · Mathematics 2025-01-24 Joshua Agterberg , Joshua Cape

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…

Methodology · Statistics 2020-05-20 Jami J. Mulgrave , Subhashis Ghosal