Robust Correlation Coefficients That Deal With Bad Leverage Points

Abstract

Consider the usual linear regression model. A well-known concern is that a bad leverage point, which is a type of outlier, can result in a poor fit to the bulk of the data, even when using any one of many robust regression estimators. In terms of measuring the strength of the association, bad leverage points can mask a strong association among the bulk of the data, and bad leverage points can suggest a strong association when in fact there is, in general, a weak association. This issue can be addressed by using an analog of Pearson’s correlation that is eliminates outliers. But this approach can have a negative impact because it eliminates what are known as good leverage points. The paper suggests a class of robust measures of association that deals with this issue.