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In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…

Statistics Theory · Mathematics 2021-12-06 Benjamin D. Robinson , Robert Malinas , Alfred O. Hero

We extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and…

Statistics Theory · Mathematics 2021-06-30 Joni Virta

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

Statistics Theory · Mathematics 2021-10-06 Lan Gao , Yingying Fan , Jinchi Lv , Qi-Man Shao

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…

Information Theory · Computer Science 2019-03-11 Guanping Lu , Jinsong Wu , Robert C. Qiu

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…

Methodology · Statistics 2025-12-11 Ritabrata Karmakar , Joydeep Chowdhury , Subhajit Dutta , Marc G. Genton

We propose a class of rank-based procedures for testing that the shape matrix $\mathbf{V}$ of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value ${\mathbf{V}}_0$; this includes,…

Statistics Theory · Mathematics 2009-09-29 Marc Hallin , Davy Paindaveine

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit…

Information Theory · Computer Science 2024-01-25 Alex Alvarado , Erik Agrell , Fredrik Brännström

This paper considers testing a covariance matrix $\Sigma$ in the high dimensional setting where the dimension $p$ can be comparable or much larger than the sample size $n$. The problem of testing the hypothesis $H_0:\Sigma=\Sigma_0$ for a…

Statistics Theory · Mathematics 2013-12-18 T. Tony Cai , Zongming Ma

We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and…

Methodology · Statistics 2018-10-05 Haoran Li , Alexander Aue , Debashis Paul

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

Large-scale modern data often involves estimation and testing for high-dimensional unknown parameters. It is desirable to identify the sparse signals, ``the needles in the haystack'', with accuracy and false discovery control. However, the…

Machine Learning · Computer Science 2021-11-08 Junhui Cai , Xu Han , Ya'acov Ritov , Linda Zhao

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Methodology · Statistics 2017-12-12 Yi-Hui Zhou

Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…

Statistics Theory · Mathematics 2024-01-23 Zeqin Lin , Guangming Pan , Peng Zhao , Jia Zhou

This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter…

Methodology · Statistics 2015-06-30 Long Feng

Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…

Statistics Theory · Mathematics 2022-12-09 J. W. Silverstein , P. L. Combettes

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…

Statistics Theory · Mathematics 2010-02-25 Jim Kuelbs , Anand N. Vidyashankar

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…

Statistics Theory · Mathematics 2015-09-15 Miles E. Lopes , Laurent J. Jacob , Martin J. Wainwright

This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity,…

Statistics Theory · Mathematics 2025-05-13 Xiaoyu Liu , Yiming Liu , Guangming Pan , Lingyue Zhang , Zhixiang Zhang

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…

Statistics Theory · Mathematics 2018-01-31 Marie Turčičová , Jan Mandel , Kryštof Eben

Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the…

Statistics Theory · Mathematics 2019-01-29 Anders Bredahl Kock , David Preinerstorfer