On Adaptive Linear Regression

Ordinary Least Squares (OLS) is omnipresent in regression modeling. Occasionally Least Absolute Deviations (LAD) or other methods are used as an alternative when there are outliers. Although some data adaptive estimators have been proposed they are typically difficult to implement. In this note, we propose an easy to compute adaptive estimator which is simply a linear combination of OLS and LAD. We demonstrate large sample normality of our estimator and show that its performance is close to best for both light tailed (e.g., normal and uniform) and heavy tailed (e.g., double exponential and t3) error distributions. We demonstrate this through 3 simulation studies and illustrate our method on state public expenditures and lutenizing hormone data sets. We conclude our method is a general and easy to use method which gives good efficiency across a wide range of error distributions. Some