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

Landon Hurley

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arXiv · 2307.10949

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

Landon Hurley

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Abstract

An inner-product Hilbert space formulation is defined over a domain of all permutations with ties upon the extended real line. We demonstrate this work to resolve the common first and second order biases found in the pervasive Kendall and Spearman non-parametric correlation estimators, while presenting as unbiased minimum variance (Gauss-Markov) estimators. We conclude by showing upon finite samples that a strictly sub-Gaussian probability distribution is to be preferred for the Kemeny $τ_κ$ and $ρ_κ$ estimators, allowing for the construction of expected Wald test statistics which are analytically consistent with the Gauss-Markov properties upon finite samples.

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Landon Hurley. 2023-07-20. Unbiased analytic non-parametric correlation estimators in the presence of ties. https://arxiv.org/abs/2307.10949

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