A finite–sample minimax regression estimator

Abstract

For the model of simple linear regression through the origin and unconditional neighborhoods (errors–in–variables) as well as conditional neighborhoods (error–free–variables) of the L¹ –type, an estimator of the slope of the regression line is derived which, among all estimators, is minimax at finite sample size and extends Huber's (1964) robust interval estimator of location

AMS 1980 subject classififcations:

• 62F35
• 62J05
• 62C20

Keywords:

• Minimax interval estimator
• One–parameter regression through the origin
• errors–in–variables
• error–free–variables
• e–contamination
• total variation
• contamination curves
• least favorable pairs