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Title: Dependence tests in high-dimensional settings under a Kronecker product covariance decomposition Authors:  Anestis Touloumis - University of Brighton (United Kingdom) [presenting]
Abstract: In many applications with high-dimensional data, the subject-specific data can be considered as realizations of large matrix-variate variables where both the rows and the columns correspond to features of interest and dependencies might occur among and between the row and column variables. For example, consider multi-tissue studies in genetics where for each subject gene expression levels are measured in multiple tissues. The subject-specific data can be written in a matrix form where the row variables correspond to genes, the column variables to tissues and the expression levels are the measurements. For inferential purposes, researchers usually employ a Kronecker product form of two covariance matrices for the dependence structure between the row and column variables; one that describes the dependence structure among the row variables and the other describes the dependence structure among the column variables. However, there is a lack of hypothesis testing procedures for the covariance matrices in high-dimensional settings. We present non-parametric tests for the identity, sphericity and diagonal sphericity hypothesis for the row (column) covariance matrix while treating the column (row) covariance matrix as nuisance.