{"ID":2823922,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24009","arxiv_id":"2512.24009","title":"An exact unbiased semi-parametric maximum quasi-likelihood framework which is complete in the presence of ties","abstract":"This paper introduces a novel quasi-likelihood extension of the generalised Kendall \\(τ_{a}\\) estimator, together with an extension of the Kemeny metric and its associated covariance and correlation forms. The central contribution is to show that the U-statistic structure of the proposed coefficient \\(τ_κ\\) naturally induces a quasi-maximum likelihood estimation (QMLE) framework, yielding consistent Wald and likelihood ratio test statistics. The development builds on the uncentred correlation inner-product (Hilbert space) formulation of Emond and Mason (2002) and resolves the associated sub-Gaussian likelihood optimisation problem under the \\(\\ell_{2}\\)-norm via an Edgeworth expansion of higher-order moments. The Kemeny covariance coefficient \\(τ_κ\\) is derived within a novel likelihood framework for pairwise comparison-continuous random variables, enabling direct inference on population-level correlation between ranked or weakly ordered datasets. Unlike existing approaches that focus on marginal or pairwise summaries, the proposed framework supports sample-observed weak orderings and accommodates ties without information loss. Drawing parallels with Thurstone's Case V latent ordering model, we derive a quasi-likelihood-based tie model with analytic standard errors, generalising classical U-statistics. The framework applies to general continuous and discrete random variables and establishes formal equivalence to Bradley-Terry and Thurstone models, yielding a uniquely identified linear representation with both analytic and likelihood-based estimators.","short_abstract":"This paper introduces a novel quasi-likelihood extension of the generalised Kendall \\(τ_{a}\\) estimator, together with an extension of the Kemeny metric and its associated covariance and correlation forms. The central contribution is to show that the U-statistic structure of the proposed coefficient \\(τ_κ\\) naturally i...","url_abs":"https://arxiv.org/abs/2512.24009","url_pdf":"https://arxiv.org/pdf/2512.24009v1","authors":"[\"Landon Hurley\"]","published":"2025-12-30T06:12:54Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}