Teaching Regression in a Nonparametric Statistics Course

Abstract

Various estimators of slope, intercept, and mean response in the simple linear regression problem are compared in terms of unbiasedness, efficiency, breakdown, and mean squared error. Theil's estimator of slope and two intercept estimators based on Theil's estimator are recommended for inclusion in nonparametrics courses as robust, efficient, and easy-to-calculate alternatives to least squares.

Key Words:

• Breakdown
• Linear regression
• Point estimation
• Robust estimation
• Theil estimator