Bias Correction for Semiparametric Regression Models
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arXiv
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| Format: | Preprint |
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2026
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| author | Zhang, Yuming Ma, Yanyuan He, Xuming Guerrier, Stéphane |
| author_facet | Zhang, Yuming Ma, Yanyuan He, Xuming Guerrier, Stéphane |
| contents | We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y|\bf{x}^{\rm T}\boldsymbolβ+m(z), ϕ\}$, which is known up to a parametric component $\boldsymbolβ$ of diverging dimension $p$, a smooth function $m(\cdot)$, and a dispersion parameter $ϕ$. Existing semiparametric literature on such models has primarily focused on semiparametric efficiency for $\boldsymbolβ$, typically treating $ϕ$ and $m(\cdot)$ as nuisances and largely ignoring their finite-sample bias. However, the finite-sample bias of standard estimators can be substantial (especially when $p$ is large relatively to $n$ and/or dispersion is high) and can seriously undermine inference for $\boldsymbolβ$. Moreover, $ϕ$ is often of direct scientific interest and requires accurate estimation. To address this gap, we propose SABRE, a simulation-based bias correction framework for this broad semiparametric model class. We establish asymptotic properties of SABRE for the subclass of generalized partially linear models, where bias reduction for $\boldsymbolβ$ and $ϕ$ can be achieved without inflating variance, and we outline how the underlying principle may be adapted more generally. Comprehensive simulation studies and a real-data application on early-stage diabetes demonstrate the empirical effectiveness of SABRE in reducing bias and improving inference. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bias Correction for Semiparametric Regression Models Zhang, Yuming Ma, Yanyuan He, Xuming Guerrier, Stéphane Methodology We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y|\bf{x}^{\rm T}\boldsymbolβ+m(z), ϕ\}$, which is known up to a parametric component $\boldsymbolβ$ of diverging dimension $p$, a smooth function $m(\cdot)$, and a dispersion parameter $ϕ$. Existing semiparametric literature on such models has primarily focused on semiparametric efficiency for $\boldsymbolβ$, typically treating $ϕ$ and $m(\cdot)$ as nuisances and largely ignoring their finite-sample bias. However, the finite-sample bias of standard estimators can be substantial (especially when $p$ is large relatively to $n$ and/or dispersion is high) and can seriously undermine inference for $\boldsymbolβ$. Moreover, $ϕ$ is often of direct scientific interest and requires accurate estimation. To address this gap, we propose SABRE, a simulation-based bias correction framework for this broad semiparametric model class. We establish asymptotic properties of SABRE for the subclass of generalized partially linear models, where bias reduction for $\boldsymbolβ$ and $ϕ$ can be achieved without inflating variance, and we outline how the underlying principle may be adapted more generally. Comprehensive simulation studies and a real-data application on early-stage diabetes demonstrate the empirical effectiveness of SABRE in reducing bias and improving inference. |
| title | Bias Correction for Semiparametric Regression Models |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.08656 |