Authors: Miodrag Lovric (Radford University, USA) and Yingcun Xia (National University of Singapore)
This article presents an accessible yet comprehensive overview of semiparametric regression models, which bridge the gap between rigid parametric and flexible nonparametric models. These models allow structured relationships to be specified parametrically while capturing unknown nonlinear patterns through nonparametric components such as kernel smoothers and splines.
Widely used forms include:
These formulations provide a flexible framework for estimating complex relationships between variables without fully specifying the data-generating process. The article also describes theoretical properties such as root-n consistency for parametric components and optimal convergence rates for nonparametric parts.
Recent advances discussed include applications in high-dimensional data, Bayesian semiparametrics using MCMC, robust techniques for outliers, and applications in functional data analysis. The integration of semiparametric modeling with machine learning tools such as deep learning and ensemble methods is also highlighted.
Software tools supporting semiparametric regression include R (e.g., mgcv for GAMs), Stata (stpm2), and others. These tools provide accessible
platforms for statisticians and applied researchers working in fields such as economics, environmental science, and public health.
For a thorough review of model types, estimation methods, theory, and modern software implementations, refer to the full article in the International Encyclopedia of Statistical Science.