Abstract:Fractional polynomials are widely used for dose-response modelling, and recent Bayesian fractional polynomial work has renewed interest in this finite model class. We propose PMM-FP, a frequentist extension of Kunchenko's polynomial maximization method to fractional-polynomial bases, developed in two parallel tracks for positive and full FP power sets under appropriate moment conditions. The main result is the closed-form variance-reduction coefficient g_2=1-gamma_3^2/(2+gamma_4) relative to OLS-FP for asymmetric non-Gaussian errors, formalised in Lean 4 and validated by Monte Carlo. On GBSG residuals, gamma_3=-1.74, gamma_4=4.91, g_2 approx 0.56: an expected standard-error gain. PMM-FP is a computationally cheap frequentist bridge to Bayesian FP modelling.
| Comments: | 47 pages, 2 figures, 6 tables |
| Subjects: | Methodology (stat.ME) |
| Cite as: | arXiv:2605.16846 [stat.ME] |
| (or arXiv:2605.16846v2 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16846 arXiv-issued DOI via DataCite |
From: Serhii Zabolotnii Dr. [view email]
[v1]
Sat, 16 May 2026 07:07:26 UTC (118 KB)
[v2]
Fri, 22 May 2026 20:07:31 UTC (127 KB)
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