Polynomial Maximization Method with Fractional Polynomial Basis: A Frequentist Bridge to Bayesian Fractional Polynomials
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910249536978944 |
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| author | Zabolotnii, Serhii |
| author_facet | Zabolotnii, Serhii |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial Maximization Method with Fractional Polynomial Basis: A Frequentist Bridge to Bayesian Fractional Polynomials Zabolotnii, Serhii Methodology 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. |
| title | Polynomial Maximization Method with Fractional Polynomial Basis: A Frequentist Bridge to Bayesian Fractional Polynomials |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.16846 |