Variable selection in measurement error models

TL;DR

This paper introduces a new penalized estimating equations framework for variable selection in measurement error models, addressing computational challenges and demonstrating asymptotic optimality and practical effectiveness.

Contribution

It develops a novel variable selection method for measurement error models using penalized estimating equations, applicable to both parametric and semi-parametric cases, with proven asymptotic properties.

Findings

Method performs as well as oracle procedures under regularity conditions.

Finite sample performance is validated through Monte Carlo simulations.

Method successfully applied to real data analysis.

Abstract

Measurement error data or errors-in-variable data have been collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of the unobservable covariates. Typically, the parameter estimation is via solving estimating equations. In addition, the construction of such estimating equations routinely requires solving integral equations, hence the computation is often much more intensive compared with ordinary regression models. Because of these difficulties, traditional best subset variable selection procedures are not applicable, and in the measurement error model context, variable selection remains an unsolved issue. In this paper, we develop a framework for variable selection in measurement error models via penalized estimating equations. We first propose a class of selection procedures for general parametric measurement error models and for general semi-parametric measurement error models, and study the asymptotic properties of the proposed procedures. Then, under certain regularity conditions and with a properly chosen regularization parameter, we demonstrate that the proposed procedure performs as well as an oracle procedure. We assess the finite sample performance via Monte Carlo simulation studies and illustrate the proposed methodology through the empirical analysis of a familiar data set.