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New Methods and Comparative Evaluations for Robust and Biased-Robust RegressionEstimation

机译：鲁棒和偏差鲁棒回归估计的新方法和比较评估

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Least squares estimation is the predominant technique for regression analysis dueto 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. The robust GM proposal from this paper is used to develop a biased-robust method. The proposed biased-robust method outperforms the published technique both in the sim.

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