Minimum Distance and Robust Estimation

Abstract

Robust and consistent estimation of the location parameter of an asymmetric distribution and general, nonlocation and scale parameter estimation problems have been vexing problems in the history of robustness studies. The minimum distance (MD) estimation method is shown to provide a heuristically reasonable mode of attack for these problems, which also leads to excellent robustness properties. Both asymptotic and Monte Carlo results for the familiar case of estimation of the location parameter of a symmetric distribution support this proposition, showing MD estimators to be competitive with some of the better estimators thus far proposed.

Key Words:

• Robust estimation
• Minimum distance
• Non-location and scale problems
• Influence curve
• Swindle