2026/05/31 by Yuming Zhang, Yanyuan Ma, Tianxi Cai +2
Mathematics · #stat.ME
arxiv created 2026/08/03 · arxiv updated 2026/08/04
We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form f\Y|\boldsymbolxT\boldsymbolβ+m(z),ϕ\, known up to a parametric component \boldsymbolβ of diverging dimension p, a smooth function m(⋅), and a dispersion parameter ϕ. The existing literature on such models has focused on semiparametric efficiency for \boldsymbolβ, treating ϕ and m(⋅) as nuisances and largely ignoring finite-sample bias. Yet this bias can be substantial, particularly when p is large relative to n or the dispersion is high, and it can seriously undermine inference for \boldsymbolβ; moreover, ϕ is often of direct scientific interest. We therefore propose SABRE, a general calibration framework for semiparametric estimation and inference, which calibrates an initial estimator against its model-implied expectation under a tractable parametric approximation to the semiparametric model. For generalized partially linear models, we show that SABRE reduces the bias of both \boldsymbolβ and ϕ, accommodates a diverging parameter dimension without sparsity, and preserves the first-order variance and semiparametric efficiency of the initial estimator; the joint construction also improves estimation and inference for m(⋅). Simulation studies and an application to Alzheimer's disease genetics association analysis demonstrate the empirical effectiveness of SABRE in reducing bias and improving inference.