Focused information criterion and model averaging for generalized additive partial linear models

TL;DR

This paper introduces a new focused information criterion and model averaging method for generalized additive partial linear models, enhancing model selection accuracy and computational efficiency with proven theoretical properties and empirical validation.

Contribution

It develops a novel FIC and FMA approach for GAPLMs, improving upon existing methods in terms of speed and reliability, supported by theoretical analysis and simulations.

Findings

Proposed procedures outperform existing methods in simulations

The estimators of linear parameters are asymptotically normal

Application to real data demonstrates practical effectiveness

Abstract

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.