We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit of the regression function and for significance of covariables, which -- in contrast to procedures from the literature -- are asymptotically not influenced by the pre-estimation of the transformation. The test statistics are asymptotically pivotal, have the same asymptotic distribution as in regression models without transformation, and standard wild bootstrap can be applied to the transformed data to conduct the tests.
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