A New Robust Regression Estimator with Self-tuning Weights

• Activity Number: 54
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): YouSung Park and DongHee Lee*+
• Companies: Korea University and Korea University
• Keywords: WSTE ; self-tuning ; efficiency ; influence function ; high breakdown point ; bad leverage outliers

Abstract

We introduce a new robust regression estimator called as weighted self-tuning robust regression estimator (WSTE). WSTE has data-adapted tuning constants which adjust by themselves and resists outliers by downweighting outlying observations systematically. We derive influence function of WSTE and show its asymptotic normality. Using five empirical datasets frequently used to assess robustness, we show that only WSTE perfectly detects known outliers in these data, compared to five competitive robust estimators. High-breakdown estimators such as the least median of squares, the least trimmed squares and the S estimators are impractical to compute exactly in large samples. However, since computation of the WSTE depends only on the number of independent variables but not on the sample size, WSTE is exactly computed and unique. Extensive simulation studies are performed using data sets with no outliers to evaluate efficiency, with large percentage of outliers to measure degree of breakdown point, and with bad leverage outliers to test bounded influence. We observe from these simulation studies that WSTE is superior to six competitive regression estimators.