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Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…

Methodology · Statistics 2025-05-27 Michael R. Schwob , Mevin B. Hooten , Nicholas M. Calzada , Timothy H. Keitt

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…

Statistics Theory · Mathematics 2018-01-23 Jinyuan Chang , Chao Zheng , Wen-Xin Zhou , Wen Zhou

Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…

Computational Geometry · Computer Science 2019-09-17 Parameswaran Raman , Jiasen Yang

This paper focuses on the prominent sphericity test when the dimension $p$ is much lager than sample size $n$. The classical likelihood ratio test(LRT) is no longer applicable when $p\gg n$. Therefore a Quasi-LRT is proposed and asymptotic…

Methodology · Statistics 2016-03-04 Zeng Li , Jianfeng Yao

This paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null…

Statistics Theory · Mathematics 2012-10-23 Alexei Onatski , Marcelo J. Moreira , Marc Hallin

In random matrix theory, the spectral distribution of the covariance matrix has been well studied under the large dimensional asymptotic regime when the dimensionality and the sample size tend to infinity at the same rate. However, most…

Statistics Theory · Mathematics 2026-03-17 Qiang Liu , Yiming Liu , Zhi Liu , Wang Zhou

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

In this paper, we propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location test. The expectation of our test is exactly zero under the null hypothesis. And we allow the dimension could…

Methodology · Statistics 2015-02-20 Long Feng , Fasheng Sun

A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…

Methodology · Statistics 2015-03-11 Måns Thulin

We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…

Statistics Theory · Mathematics 2018-06-18 Ahmed El Alaoui , Michael I. Jordan

High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…

Methodology · Statistics 2026-04-16 Long Feng

Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…

Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…

Methodology · Statistics 2018-02-27 S. Rao Jammalamadaka , Gyorgy Terdik

The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…

Statistics Theory · Mathematics 2023-09-20 Michael Celentano , Andrea Montanari , Yuting Wei

We study the high-dimensional two-sample location problem under elliptical symmetry with arbitrary dependence in the scatter matrix. Existing spatial-sign procedures are attractive for heavy-tailed data, but their null calibration is tied…

Methodology · Statistics 2026-05-06 Long Feng , Hongfei Wang

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…

Information Theory · Computer Science 2017-09-11 Wajeeha Nafees , Zubair Khalid , Rodney A. Kennedy , Jason D. McEwen

In this paper, we provide $R$-estimators of the location of a rotationally symmetric distribution on the unit sphere of $\R^k$. In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric…

Applications · Statistics 2012-03-28 Christophe Ley , Yvik Swan , Baba Thiam , Thomas Verdebout

Two-sample hypothesis testing is a fundamental problem with various applications, which faces new challenges in the high-dimensional context. To mitigate the issue of the curse of dimensionality, high-dimensional data are typically assumed…

Methodology · Statistics 2026-04-06 Jiaqi Gu , Ruoxu Tan , Guosheng Yin

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

Statistics Theory · Mathematics 2022-07-20 Paavo Sattler , Markus Pauly

Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…

Methodology · Statistics 2021-05-04 Hao Chen , Yin Xia