Bias Correction for Semiparametric Regression Models

2026-05-08

AI Summary

This study addresses the substantial finite-sample bias that arises in semiparametric regression models when estimating high-dimensional or discrete parameters, which can severely compromise statistical inference for both the regression coefficients β and the discrete parameter φ. To tackle this issue, the authors propose SABRE—a simulation-based bias correction framework that, for the first time, jointly corrects the finite-sample biases of β and φ in a systematic manner. By integrating asymptotic theory for generalized partially linear models, SABRE establishes a unified correction framework accommodating diverging-dimensional parametric and nonparametric components, effectively reducing bias without inflating variance. Extensive simulations and an analysis of early diabetes data demonstrate that SABRE markedly enhances estimation accuracy and the reliability of statistical inference.

Abstract

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.

Problem

• bias correction
• semiparametric regression
• finite-sample bias
• dispersion parameter
• high-dimensional inference

Innovation

• bias correction
• semiparametric regression
• SABRE
• finite-sample bias
• diverging dimension