A Unified Nonparametric Test of Transformations on Distribution Functions with Nuisance Parameters

This paper proposes a simple unified approach to testing transformations on cumulative distribution functions (CDFs) with nuisance parameters. We consider testing general parametric transformations on two CDFs, and then generalize the test for multiple CDFs. We construct the test using a numerical bootstrap method which can easily be implemented. The proposed test is shown to be asymptotically size controlled and consistent. Monte Carlo simulations and an empirical application show that the test performs well on finite samples.