Robust measures of association in the correlation model

In the correlation model, the classical coefficient of multiple determination 2 is a measure of association between the dependent random variable Y and the random vector of independent variables x. Slight departures from normality, however, can have a pronounced effect on the measure. In the regression model robust estimates of the regression coefficients are less sensitive to outlying points than least squares estimates. These estimates are often obtained by minimizing an objective (dispersion) function. For such robust estimates, the proportion of explained dispersion is a natural analogue to the statistic R2. Although this statistic is generally not robust, it leads to robust statistics which are consistent estimates of functionals in the correlation model. These functionals are robust measures of association between Y and x. They are efficiently robust and have bounded influence provided the robust estimator on which they are based has bounded influence.