Bergsma--Dassios sign covariance with ties: a nonnegative decomposition and sharp bounds

Wicher Bergsma, Angelos Dassios

We construct tie-symmetrised extensions $\tilde{D}$ and $\tilde{R}$ of the unnormalised Hoeffding and Blum--Kiefer--Rosenblatt functionals $D$ and $R$ and prove, for every re…