2 problems

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Bergsma–Dassios–Yanagimoto conjecture on $\tau^*$ and independence
Let $(X_1,X_2)$ be a random vector with an arbitrary distribution on $\mathbb{R}^2$ , and let $h_{\tau^*}$ be the symmetric kernel defining Bergsma–Dassios–Yanagimoto's rank correla…
Conjectureopenindependence-testing rank-correlations u-statisticsarXiv posted 2 days ago
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Rate-optimality of Kendall's tau tests for elliptical alternatives
Let $T_\tau$ denote the unbiased estimator of signal strength formed from the kernel associated with Kendall's tau. The alternatives are high-dimensional dependence alternatives fr…
Conjectureopenhigh-dimensional-statistics independence-testing rank-correlationsarXiv posted 2 days ago

Bergsma–Dassios–Yanagimoto conjecture on τ∗\tau^*τ∗ and independence