E2023003 2023-02-20
Zhenting Sun
China Center for Economic Research
National School of Development
Peking University
Abstract
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 param-eters. 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.
Keywords: Unified test, transformations on CDFs, nuisance parameters, numerical boot-strap
