New Methods and Comparative Evaluations for Robust and Biased-Robust Regression Estimation,
Abstract
Least squares estimation is the predominant technique for regression analysis due to its universal acceptance, elegant statistical properties, and computational simplicity. Unfortunately, the statistical properties that make least squares so powerful depend on several assumptions that are often violated using real data. The normally distributed errors assumption, which enables tests of regressor significance, is invalid if only a single outlying observation occurs in the data. Robust regression methods are less sensitive to outliers than the method of least squares. Recently published techniques suggest improved robust estimation performance. These robust methods are comparatively evaluated using Monte Carlo simulation. Evaluation results lead to new proposals from a class of robust methods called GM-estimators. GM-estimation constrains the excess influence that observations outlying in the regressor space have on parameter estimates, enabling fits to the majority of the data regardless of outlier location. Several GM-estimation proposals are developed and evaluated. Two preferred GM proposals are compared with top performing existing robust methods in a comprehensive study of outlier and nonoutlier configurations. The best performing methods are an existing technique called MM-estimation and a proposed GM technique. Least squares estimation can also be adversely impacted by dependencies among the regressors called multicollinearity. The resulting least squares parameter estimates can change significantly with only slight changes in the data. The combined outlier-multicollinearity problem occurs frequently in routine data. Methods that address this problem effectively robust estimation techniques.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1995
- Accession Number
- ADA298578
Entities
People
- James R. Simpson
Organizations
- Air Force Institute of Technology