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) in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters. The critical values are obtained through a numerical bootstrap method which can easily be implemented in practice. Under suitable conditions, the proposed test is shown to be asymptotically size controlled and consistent. The local power property of the test is established. Finally, Monte Carlo simulations and an empirical study show that the test performs well on finite samples.