Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data

TL;DR

This paper introduces a bias-corrected GEE estimation method with a smooth-threshold variable selection procedure for single-index models with clustered data, ensuring consistent variable identification even with misspecified correlation structures.

Contribution

It develops a novel bias-corrected GEE approach combined with a computationally simple variable selection method that achieves the oracle property in clustered data settings.

Findings

Estimator performs well in simulations

Method correctly identifies significant variables

Applicable to real clustered data examples

Abstract

In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations, bias-correction is necessary when general working correlation matrices are used in the estimating equations. Our variable selection procedure based on smooth-threshold estimating equations \citep{Ueki-2009} can automatically eliminate irrelevant parameters by setting them as zeros and is computationally simpler than alternative approaches based on shrinkage penalty. The resulting estimator consistently identifies the significant variables in the index, even when the working correlation matrix is misspecified. The asymptotic property of the estimator is the same whether or not the nonzero parameters are known (in both cases we use the same estimating equations), thus achieving the oracle property in the sense of \cite{Fan-Li-2001}. The finite sample properties of the estimator are illustrated by some simulation examples, as well as a real data application.