Robust Regression: Methods and Applications

This lecture introduces robust and resistant methods in linear models, focusing on the limitations of the Least Squares Estimator (LSE) in the presence of extreme observations. The instructor discusses the concept of robustness and resistance in regression models, highlighting the importance of not being strongly affected by changes in data or departures from the distribution. Various robust/ resistant procedures are explored, such as trimmed means, weighted estimates, and M-Estimators. The lecture also covers the asymptotic relative efficiency (ARE) and its implications in linear models, providing examples to illustrate the concept. Additionally, practical applications, like Mallow's Rule, are presented to guide the analysis when faced with discrepancies between robust and standard methods.