Regression: Comparing Predictors and Groups of Predictors Based on a Robust Measure of Association

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Let ρj be Pearson’s correlation between Y and Xj (j = 1, 2). A problem that has received considerable attention is testing H0: ρ1 = ρ2. A well-known concern, however, is that Pearson’s correlation is not robust (e.g., Wilcox, 2005), and the usual estimate of ρj , rj has a finite sample breakdown point of only 1/n. The goal in this paper is to consider extensions to situations where Pearson’s correlation is replaced by a particular robust measure of association. Included are results where there are p > 2 predictors and the goal to compare any two subsets of m < p predictors.