Document Type : original

Author

• Mahdieh Bayati

University of Qom

Abstract

This study generalizes the joint empirical likelihood (JEL) which is named the joint penalized empirical likelihood(JPEL) and presents a comparative analysis of two innovative empirical likelihood methods: the restricted penalized empirical likelihood (RPEL) and the joint penalized empirical likelihood. These methods extend traditional empirical likelihood approaches by integrating criteria based on the minimum variance and unbiasedness of the estimator equations. In RPEL, estimators are obtained under these two criteria, while JPEL facilitates the joint application of the estimator equations used in RPEL, allowing for broader applicability.\\
We evaluate the effectiveness of RPEL and RJEL in regression models through simulation studies, and evaluate the performance of RPEL and JPEL, focusing on parameter accuracy, model selection (as measured by the Empirical Bayesian Information Criterion), predictive accuracy (Mean Square Error), and robustness to outliers. Results indicate that RPEL consistently outperforms JPEL across all criteria, with RPEL yielding simpler models and more reliable estimates, particularly as sample sizes increase. These findings suggest that RPEL provides greater stability and interpretability for regression models, making it a superior choice over JPEL for the scenarios tested in this study.

Keywords

• Empirical likelihood
• restricted penalized empirical likelihood
• restricted joint empirical likelihood
• estimating equations
• Gibbs sampling
• MCMC

Main Subjects

• Bayesian Computation Statistics