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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Master in Mathematics

Author:
Roman Nagurski

Title:
A bias corrected estimator for distance correlation

Supervisors:
Jan JOHANNES and Dominic Edelmann (DKFZ)

Abstract:
In this thesis asymptotic properties of two estimators for the squared distance covariance of random vectors in arbitrary dimensions are presented. Distance covariance is a dependency measure which was first studied by Székely, Rizzo and Bakirov (2007). We are going to present two consistent estimators, mainly focussing on the second. We derive its unbiasedness and show that it is a U-statistic. Using U-statistic theory, we derive strong consistency and sysmptotic properties. In our application, simulated as well as real data are explored. We compare the permutation-based distance covariance test with a corresponding test based on Pearson correlation.

Reference:
Székely, Rizzo, et Bakirov. Measuring and testing dependence by correlation of distances, The Annals of Statistics, 35(6):2769–2794, 2007.