Bias Correction for Semiparametric Regression Models

TL;DR

This paper introduces SABRE, a simulation-based bias correction method for broad semiparametric regression models, improving finite-sample inference for parameters of scientific interest.

Contribution

It develops a bias correction framework that reduces finite-sample bias in semiparametric models without increasing variance, applicable to generalized partially linear models.

Findings

SABRE effectively reduces bias in parameter estimates.

Simulation studies show improved inference accuracy.

Application to diabetes data demonstrates practical utility.

Abstract

We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y|\bf{x}^{\rm T}\boldsymbol{\beta}+m(z), \phi\}$, which is known up to a parametric component $\boldsymbol{\beta}$ 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 $\boldsymbol{\beta}$, 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 $\boldsymbol{\beta}$. 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 $\boldsymbol{\beta}$ 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.