Seminar: "Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure"

AUEB STATISTICS SEMINAR SERIES MARCH 2022

Anestis Touloumis (School of Architecture, Technology and Engineering, University of Brighton, UK)

Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure

ABSTRACT:

The term transposable data refers to matrix-valued random variables that treat the rows and columns as two distinct sets of variables of interest and dependencies might occur among and between the row and column variables. The matrix-variate normal distribution is a popular model for transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices, one for each of row and column variables without ignoring the dependence between the row and column variables. However, there is a lack of testing procedures for these covariance matrices in high-dimensional settings. We propose tests that assess the sphericity, identity, and diagonality hypotheses for the row (column) covariance matrix in a high-dimensional setting, while treating the column (row) dependence structure as a "nuisance" parameter. The proposed tests are robust to normality departures, provided that the Kronecker product dependence structure holds. Simulation studies and real data analyses are conducted to demonstrate the proposed method. Software implementing the methodology is available in the Bioconductor package HDTD.
This is joint work with John Marioni (University of Cambridge) and Simon Tavaré (Columbia University).

You can watch a video of the presentation here.