A Bernstein-smoothed lower-tail Spearman's rho keeps the classical estimator's asymptotic normality while cutting finite-sample mean squared error by up to about 70 percent in deep-tail simulations.
Hudaverdi and Susam [8] adapted the same Bernstein smoothing idea to weighted Cramér– von Mises statistics and documented substantial power gains across a broad spectrum of copulas
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On the Bernstein-smoothed lower-tail Spearman's rho estimator
A Bernstein-smoothed lower-tail Spearman's rho keeps the classical estimator's asymptotic normality while cutting finite-sample mean squared error by up to about 70 percent in deep-tail simulations.