An Adaptive Multiple Regression Procedure Based on M-Estimators

Abstract

Multiple linear regression techniques that are resistant to changes in a small fraction of the data have been proposed and investigated in recent literature. This paper develops a regression procedure based on M-estimators that is adaptive in nature. That is, after a preliminary fit, an attempt is made to assess the nature of the distribution of the errors. Based on this assessment, an appropriate M-estimator is then chosen and the final multiple linear regression equation is computed. The rule's resistance to a few outlying data points is demonstrated with a classical data set on the stack loss of a plant converting ammonia to nitric acid. The adaptive procedure's excellent performance characteristics over a broad class of distributions is shown in a Monte Carlo study.

KEY WORDS:

• Linear regression
• M-estimator
• Adaptive
• Robust estimation