Visual assessment of matrix-variate normality

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Australian & New Zealand Journal of Statistics Pub Date : 2023-06-17 DOI:10.1111/anzs.12388

Nikola Počuča, Michael P.B. Gallaugher, Katharine M. Clark, Paul D. McNicholas

引用次数: 1

Abstract

In recent years, the analysis of three-way data has become ever more prevalent in the literature. It is becoming increasingly common to analyse such data by means of matrix-variate distributions, the most prevalent of which is the matrix-variate normal distribution. Although many methods exist for assessing multivariate normality, there is a relative paucity of approaches for assessing matrix-variate normality. Herein, a new visual method is proposed for assessing matrix-variate normality by means of a distance–distance plot. In addition, a testing procedure is discussed to be used in tandem with the proposed visual method. The proposed approach is illustrated via simulated data as well as an application on analysing handwritten digits.

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矩阵变量正态性的可视化评估

近年来，对三元数据的分析在文献中变得越来越普遍。通过矩阵变量分布来分析这些数据变得越来越普遍，其中最普遍的是矩阵变量正态分布。尽管存在许多评估多元正态性的方法，但评估矩阵多元正态的方法相对较少。本文提出了一种新的视觉方法，通过距离-距离图来评估矩阵变量的正态性。此外，还讨论了与所提出的视觉方法一起使用的测试程序。通过模拟数据以及在手写数字分析中的应用，说明了所提出的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Australian & New Zealand Journal of Statistics 数学-统计学与概率论

CiteScore

1.30

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.