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We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary…

Data Analysis, Statistics and Probability · Physics 2012-10-26 Glen Cowan , Kyle Cranmer , Eilam Gross , Ofer Vitells

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

We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…

Statistics Theory · Mathematics 2026-05-18 Dietmar Ferger

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

Statistics Theory · Mathematics 2019-12-16 Zeng Li , Qinwen Wang , Runze Li

We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…

Mathematical Physics · Physics 2011-01-18 Mariya Shcherbina

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Stepan Mazur , Nestor Parolya

We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution of the…

Probability · Mathematics 2023-08-23 Shu Kanazawa , Khanh Duy Trinh

This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…

Statistics Theory · Mathematics 2019-02-12 Natsumi Makigusa , Kanta Naito

We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under the null hypothesis. While so far the likelihood ratio statistic has only been studied for normal populations,…

Statistics Theory · Mathematics 2024-08-01 Nina Dörnemann

It is well known that, under some assumptions, the limit distribution of random block matrices and their partial transposition converges to the distributions of random variables in some noncommutative probability space. Using free…

Quantum Physics · Physics 2023-03-21 Zhi Yin , Liang Zhao

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…

Statistics Theory · Mathematics 2021-03-29 Michael Bell , Yuval Kochman

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

Statistics Theory · Mathematics 2022-08-11 Aishwarya Bhaskaran , Matt P. Wand

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…

Statistics Theory · Mathematics 2022-05-17 Lin Zhou , Yun Wei , Alfred Hero

Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…

Statistics Theory · Mathematics 2024-05-14 Rahul Singh , Neeraj Misra

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…

Probability · Mathematics 2015-06-26 L. Pastur

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

Methodology · Statistics 2016-07-14 Ignacio Alvarez , Jarad Niemi , Matt Simpson

Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…

Statistics Theory · Mathematics 2026-04-15 Ziang Niu , Zhimei Ren

It is shown that a noncentral Wishart mixture of noncentral Wishart distributions with the same degrees of freedom yields a noncentral Wishart distribution, thereby extending the main result of Jones and Marchand [Stat 10 (2021), Paper No.…

Statistics Theory · Mathematics 2026-03-10 Christian Genest , Anne MacKay , Frédéric Ouimet

Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…

Signal Processing · Electrical Eng. & Systems 2020-01-07 Florent Chatelain , Nicolas Le Bihan , Jonathan H. Manton

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

Statistics Theory · Mathematics 2022-09-12 Sherzod M. Mirakhmedov