AN ALTERNATIVE DERIVATION OF ALIGNED RANK-TESTS FOR REGRESSION

A new method for deriving aligned rank tests and their efficacy is presented. The approach makes use of the asymptotic version of the rank transformation. Under the null hypothesis, the transformed data conform to a linear model and thus an F-test statistic based on the transformed data is easily constructed. Properties of the empirical process are then used to show that the F-statistic based on the rank transformation is asymptotically equivalent to the F-statistic based on the asymptotic version of the rank transformation. This approach has a strong heuristic flavor making it more suitable for classroom presentation.