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

在转换回归模型中，在对回归模型进行协变量拟合和转换后的响应之前先对响应进行转换。我们假设这样一个模型，其中误差与协变量无关，并且回归函数是非参数建模的。我们建议根据非参数转换估计量与参数类别之间的距离，对参数转换类别的拟合优度进行测试。在半参数模型有效性的零假设下以及在局部替代条件下，我们提出了渐近理论。建议使用自举算法以应用测试。我们还考虑了相关假设，以区分参数转换类与“真实”转换的大与小距离。