  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 computational times for both methods under
different dependence structures. Under conditions of independence or
near-independence, the V-estimates are biased, while the U-estimator frequently
cannot be computed due to negative values. To address this challenge, a convex
linear combination of the former estimators is proposed and studied, yielding
good results regardless of the level of dependence.
