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In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…

Statistics Theory · Mathematics 2017-08-16 Yinchu Zhu , Jelena Bradic

This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…

Statistics Theory · Mathematics 2021-01-25 Weiming Li , Qinwen Wang , Jianfeng Yao , Wang Zhou

The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we…

Methodology · Statistics 2015-11-06 Tung-Lung Wu , Ping Li

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

Methodology · Statistics 2023-01-12 Zhipeng Lou , Xianyang Zhang , Wei Biao Wu

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

Statistics Theory · Mathematics 2026-01-28 Annika Betken , Herold Dehling

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…

Machine Learning · Statistics 2018-06-08 Michael Hornstein , Roger Fan , Kerby Shedden , Shuheng Zhou

In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…

Statistics Theory · Mathematics 2019-02-12 Changbo Zhu , Shun Yao , Xianyang Zhang , Xiaofeng Shao

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Machine Learning · Statistics 2024-10-29 Hanwen Huang , Peng Zeng

In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K…

Statistics Theory · Mathematics 2024-04-11 Rémi Beisson , Pascal Vallet , Audrey Giremus , Guillaume Ginolhac

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…

Methodology · Statistics 2015-10-21 Xianyang Zhang

In randomized experiments, treatment and control groups should be roughly the same--balanced--in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests?…

Methodology · Statistics 2008-08-29 Ben B. Hansen , Jake Bowers

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…

Statistics Theory · Mathematics 2015-04-28 Jiang Hu , Zhidong Bai , Chen Wang , Wei Wang

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

Methodology · Statistics 2019-11-22 Soham Sarkar , Rahul Biswas , Anil K. Ghosh

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…

Machine Learning · Computer Science 2024-10-10 Agus Hartoyo , Jan Argasiński , Aleksandra Trenk , Kinga Przybylska , Anna Błasiak , Alessandro Crimi

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

Methodology · Statistics 2020-11-10 Linjun Zhang , Rong Ma , T. Tony Cai , Hongzhe Li

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…

Methodology · Statistics 2018-09-25 Zongliang Hu , Tiejun Tong , Marc G. Genton

In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…

Statistics Theory · Mathematics 2026-02-16 Tianxing Mei , Chen Wang , Jianfeng Yao

Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $\Sigma$ with an additional assumption that $\Sigma$ can be represented as a sum of a few Kronecker products…

Statistics Theory · Mathematics 2024-06-18 Nikita Puchkin , Maxim Rakhuba

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

Methodology · Statistics 2013-01-17 Nicolas Städler , Sach Mukherjee

Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices…

Statistics Theory · Mathematics 2018-01-23 Weiming Li , Zeng Li , Jianfeng Yao