Improving Estimation Efficiency In Structural Equation Models By An Easy Empirical Likelihood Approach

TL;DR

This paper introduces an easy empirical likelihood method to improve estimation efficiency in structural equation models by incorporating side information, resulting in estimators with reduced variance.

Contribution

It develops EL-weighted estimators using estimated constraints and growing constraints, enhancing efficiency in SEMs with side information.

Findings

EL-weighted estimators have lower variance in SEMs.

The method effectively incorporates side information.

Simulation results confirm efficiency gains.

Abstract

In this article, we construct empirical likelihood (EL)-weighted estimators of linear functionals of a probability measure in the presence of side information. Motivated by nuisance parameters in semiparametric models with possibly infinite dimensions, we consider the use of estimated constraint functions and allow the number of constraints to grow with the sample size. We study the asymptotic properties and efficiency gains. The results are used to construct improved estimators of parameters in structural equation models. The EL-weighted estimators of parameters are shown to have reduced variances in a SEM in the presence of side information of stochastic independence of the random error and random covariate. Some simulation results on efficiency gain are reported.