Improved distance correlation estimation
Blanca E. Monroy-Castillo, M.A, J\'acome, Ricardo Cao

TL;DR
This paper compares two estimators of distance correlation, evaluates their efficiency, and proposes a convex combination to improve estimation accuracy across different dependence levels.
Contribution
It introduces a combined estimator that improves distance correlation estimation, addressing biases and computational issues of existing methods.
Findings
V-estimates are biased under independence.
U-estimator often cannot be computed due to negative values.
The combined estimator yields better results across dependence levels.
Abstract
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient, the most important is that distance correlation equals zero if and only if the random vectors are independent. There are two different estimators of the distance correlation available in the literature. The first one, proposed by Sz\'ekely et al. (2007), is based on an asymptotically unbiased estimator of the distance covariance which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance proposed in Sz\'ekely et al. (2014), proved to be an U-statistic by Sz\'ekely and Huo (2016). This study evaluates their efficiency (mean squared error) and compares…
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Taxonomy
TopicsNeural Networks and Applications
