Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

• 成果类型: Article
• 署名作者: Bondell, Howard D.; Stefanski, Leonard A.
• 署名单位: North Carolina State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.779847
• 发表日期: 2013
• 页码: 644-655
• 关键词: least-squares estimation; high breakdown-point; estimators; models; gmm

摘要

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we, develop and study a linear regression estimator that comes close. Efficiency is obtained from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers.