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In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…

Methodology · Statistics 2023-03-22 Kwun Chuen Gary Chan , Hok Kan Ling , Chuan-Fa Tang , Sheung Chi Phillip Yam

Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…

Statistics Theory · Mathematics 2007-06-13 Hongtu Zhu , Heping Zhang

Most machine learning models operate under the assumption that the training, testing and deployment data is independent and identically distributed (i.i.d.). This assumption doesn't generally hold true in a natural setting. Usually, the…

Machine Learning · Computer Science 2021-12-14 Kumud Lakara , Akshat Bhandari , Pratinav Seth , Ujjwal Verma

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Methodology · Statistics 2020-02-25 Steffen Betsch , Bruno Ebner

We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is…

Methodology · Statistics 2025-06-30 Tongyu Li , Jonas Mueller , Fang Yao

In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…

Statistics Theory · Mathematics 2023-03-16 Yangfan Zhang , Runmin Wang , Xiaofeng Shao

Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…

Methodology · Statistics 2024-04-16 Robin Dunn , Aditya Gangrade , Larry Wasserman , Aaditya Ramdas

We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint…

Applications · Statistics 2018-10-12 Pavel Krupskii , Marc G. Genton

We derive the asymptotic distribution of the spatial Cram'{e}r--von Mises statistic for testing bivariate independence in stationary random fields on $\mathbb{R}^2$ under polynomial $\beta$-mixing dependence, and document the Python…

Methodology · Statistics 2026-05-20 Marco Mandap

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…

Signal Processing · Electrical Eng. & Systems 2022-06-14 Martin Gölz , Abdelhak M. Zoubir , Visa Koivunen

Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…

Computational Geometry · Computer Science 2020-04-14 Panagiotis Sidiropoulos

We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit…

Statistics Theory · Mathematics 2017-11-21 Norbert Henze , María Dolores Jiménez-Gamero

Comparing multivariate yield quality distributions across spatially referenced agricultural fields is complicated by two pervasive features: non-normality and spatial autocorrelation. Classical procedures such as ANOVA, MANOVA, and standard…

Methodology · Statistics 2026-03-03 Marco Mandap

Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built…

Methodology · Statistics 2016-10-10 Noel Cressie , Andrew Zammit-Mangion

Multivariate functional data has received considerable attention but testing for equality of mean surfaces and its profile has limited progress. The existing literature has tested equality of either mean curves of univariate functional…

Methodology · Statistics 2019-03-07 Jin Yang , Tao Zhang , Chunling Liu , Kam Chuen Yuen , Aiyi Liu

Many data problems contain some reference or normal conditions, upon which to compare newly collected data. This scenario occurs in data collected as part of clinical trials to detect adverse events, or for measuring climate change against…

Methodology · Statistics 2025-02-05 Annalisa Calvi , Ursula Laa , Dianne Cook

In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…

Methodology · Statistics 2017-07-24 Rafael S. Erbisti , Thais C. O. Fonseca , Mariane B. Alves

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Statistics Theory · Mathematics 2022-02-17 Bhaswar B. Bhattacharya , Rajarshi Mukherjee

We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…

Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…

Methodology · Statistics 2026-04-07 Akin Anarat , Holger Schwender