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An inner-product Hilbert space formulation is defined over a domain of allpermutations with ties upon the extended real line. We demonstrate this work toresolve the common first and second order biases found in the pervasive Kendalland Spearman non-parametric correlation estimators, while presenting asunbiased minimum variance (Gauss-Markov) estimators. We conclude by showingupon finite samples that a strictly sub-Gaussian probability distribution is tobe preferred for the Kemeny $\tau_{\kappa}$ and $\rho_{\kappa}$ estimators,allowing for the construction of expected Wald test statistics which areanalytically consistent with the Gauss-Markov properties upon finite samples.

Unbiased analytic non-parametric correlation estimators in the presence of ties