🤖 AI Summary
This paper addresses inference on general parameter transformations of cumulative distribution functions (CDFs) in the presence of nuisance parameters. We propose a unified, nonparametric, asymptotically size-controlled testing framework applicable to joint inference on one-, two-, and multi-sample CDFs. The method constructs test statistics via numerical bootstrap, obviating analytical critical value derivation and ensuring implementation simplicity. We establish theoretical guarantees of asymptotic size control and consistency. Monte Carlo simulations and empirical analyses demonstrate strong finite-sample robustness and high statistical power. Our key contribution is the first unified, nonparametric, asymptotically valid, and structure-free test for transformations of CDFs with nuisance parameters—overcoming the restrictive functional-form and parametric-structure assumptions inherent in conventional approaches.
📝 Abstract
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.
