Specification testing in semi-parametric transformation models

Abstract In transformation regression models, the response is transformed before fitting a model to covariates and response. We assume such where errors are independent from function modeled nonparametrically. suggest test for goodness-of-fit of parametric class based on distance between nonparametric estimator class. present asymptotic theory under null hypothesis validity semi-parametric local alternatives. A bootstrap algorithm suggested in order apply test. also consider relevant hypotheses distinguish large small distances ‘true’ transformation.