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Related papers: Testing in high-dimensional spiked models

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Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…

Methodology · Statistics 2021-01-28 Sergey Tarima , Nancy Flournoy

We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of…

Statistics Theory · Mathematics 2009-01-22 N. Raj Rao , James A. Mingo , Roland Speicher , Alan Edelman

Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…

Probability · Mathematics 2024-10-22 Tiefeng Jiang , Yongcheng Qi

We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…

Statistics Theory · Mathematics 2016-12-05 Dennis Leung , Mathias Drton

Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured…

Methodology · Statistics 2022-02-28 Vladimir Vutov , Thorsten Dickhaus

In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population…

Statistics Theory · Mathematics 2021-04-09 Yanqing Yin

We develop a nonparametric two-sample test for distributions supported on the cone of symmetric positive definite matrices. The procedure relies on the Wishart kernel density estimator (KDE) introduced by Belzile et al. (2025), whose…

Statistics Theory · Mathematics 2026-03-17 Frédéric Ouimet

We study the computational task of detecting and estimating correlated signals in a pair of spiked matrices $$ X=\tfrac{\lambda}{\sqrt{n}} xu^{\top}+W, \quad Y=\tfrac{\mu}{\sqrt{n}} yv^{\top}+Z $$ where the spikes $x,y$ have correlation…

Statistics Theory · Mathematics 2025-12-03 Zhangsong Li

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

Methodology · Statistics 2018-10-23 Mingjuan Zhang , Yong He , Cheng Zhou , Xinsheng Zhang

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…

Statistics Theory · Mathematics 2026-03-26 Jianwei Hu , Jingfei Zhang , Jianhua Guo , Ji Zhu

In applied settings, tests of hypothesis where a nuisance parameter is only identifiable under the alternative often reduces into one of Testing One Hypothesis Multiple times (TOHM). Specifically, a fine discretization of the space of the…

Methodology · Statistics 2022-04-06 Sara Algeri , David A. van Dyk

Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…

Numerical Analysis · Computer Science 2012-11-07 Jonathan Touboul

Motivated by dimension reduction in regression analysis and signal detection, we investigate the order determination for large dimension matrices including spiked models of which the numbers of covariates are proportional to the sample…

Methodology · Statistics 2019-11-01 Yicheng Zeng , Lixing Zhu

Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…

Probability · Mathematics 2025-02-19 Bertrand Stone , Fan Yang , Jun Yin

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the…

Statistics Theory · Mathematics 2013-06-21 Alexei Onatski , Marcelo J. Moreira , Marc Hallin

We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…

Machine Learning · Statistics 2015-10-16 Zhuoran Yang , Yang Ning , Han Liu

This paper considers testing the covariance matrices structure based on Wald's score test in large dimensional setting. The hypothesis $H_0: \Sigma =\Sigma_0 $ for a given matrix $\Sigma_0$, which covers the identity hypothesis test and…

Methodology · Statistics 2016-03-01 Dandan Jiang , QiBin Zhang

The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…

Probability · Mathematics 2021-08-24 Heidar Eyjolfsson , Dag Tjøstheim

The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…

Mathematical Physics · Physics 2014-09-23 Santosh Kumar

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…

Statistics Theory · Mathematics 2024-10-07 Riccardo De Santis , Jelle J. Goeman , Samuel Davenport , Jesse Hemerik , Livio Finos