Bias Correction for Semiparametric Regression Models

We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y\mathrm{\mid }{\mathbf{x}}^{\mathrm{T}}\mathit{\beta }+\mathbf{m}(\mathbf{z}),\mathbf{\phi }\}$, which is known up to a parametric component $\mathit{\beta }$ of diverging dimension $p$, a smooth function $m(\cdot )$, and a dispersion parameter $\phi$. Existing semiparametric literature on such models has primarily focused on semiparametric efficiency for $\mathit{\beta }$, typically treating $\phi$ 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 $\mathit{\beta }$. Moreover, $\phi$ 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 $\mathit{\beta }$ and $\phi$ 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.