A diagonality measure for covariance matrices. Statistical applications.

C. Matrán Bea, D. Rodríguez Vítores

We introduce a new measure to evaluate approximation to diagonality of a positive definite matrix with a view to its application to the problem of common principal directions. The proposal arises from ideas related to optimal L2 transportation between probability distributions, linked to dependence structures, summarized here through Gelbrich's bound. The measure aims at assessing the adequacy of certain characteristics - the observed variables - for the comparison of distributions, and the point of view is to measure the agreement of the principal directions of the associated covariance matrices. The measure is defined from a matrix inequality on the trace, by means of an appropriate normalization, and its analysis includes its asymptotic behavior from random samples and its performance with real data and simulations.

Keywords: Wasserstein distance, common principal directions, multivariate analysis, trace operators, matrix differential calculus, Gelbrich bound

Scheduled

Multivariate Analysis II
June 8, 2022  5:20 PM
Cloister room

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