Mean Equality Tests for High-Dimensional and Higher-Order Data with k-Self Similar Compound Symmetry Covariance Structure

Symmetry

Ricardo Leiva¹  Anuradha Roy² 

[1] Departamento de Matemática, Facultad de Ciencias Económicas, Universidad Nacional de Cuyo, Mendoza 5500, Argentina;Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA;

关键词: array-variate data;    eigenblock;    high dimensional data;    Wishart distribution;    Hotelling’s T2 statistic;    Lawley–Hotelling trace distribution;   

DOI  :  10.3390/sym14020291

来源: DOAJ

【 摘 要 】

An extension of the $D^2$ test statistic to test the equality of mean for high-dimensional and k-th order array-variate data using k-self similar compound symmetry (k-SSCS) covariance structure is derived. The k-th order data appear in many scientific fields including agriculture, medical, environmental and engineering applications. We discuss the property of this k-SSCS covariance structure, namely, the property of Jordan algebra. We formally show that our $D^2$ test statistic for k-th order data is an extension or the generalization of the $D^2$ test statistic for second-order data and for third-order data, respectively. We also derive the $D^2$ test statistic for third-order data and illustrate its application using a medical dataset from a clinical trial study of the eye disease glaucoma. The new test statistic is very efficient for high-dimensional data where the estimation of unstructured variance-covariance matrix is not feasible due to small sample size.

【 授权许可】

Unknown