Estimators of the multiple correlation coefficient: Local robustness and confidence intervals

Abstract

Many robust regression estimators are defined by minimizing a measure of spread of the residuals. An accompanying R 2-measure, or multiple correlation coefficient, is then easily obtained. In this paper, local robustness properties of these robust R 2-coefficients are investigated. It is also shown how confidence intervals for the population multiple correlation coefficient can be constructed in the case of multivariate normality.