In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on stritcly increasing and continuous transformations. In view of estimating the tranformation parameter, we use a minimum distance approach and show the uniform consistency of the estimator under mild conditions. The boundary curve, i.e. the regression function, is estimated applying a smoothed version of a local constant approximation for which we also prove the uniform consistency. We deal with both cases of random covariates and deterministic (fixed) design points. To highlight the applicability of the procedures and to demonstrate their performance, the small sample behavior is investigated in a simulation study using the so-called Yeo-Johnson transformations.

中文翻译：

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半参数变换边界回归模型

在具有单边误差的非参数回归模型的背景下，我们考虑响应变量的参数变换，以获得误差和协变量之间的独立性。我们在本文中重点讨论严格递增和连续变换。鉴于估计变换参数，我们使用最小距离方法并在温和条件下显示估计器的均匀一致性。边界曲线，即回归函数，是应用局部常数近似的平滑版本估计的，我们也证明了统一一致性。我们处理随机协变量和确定性（固定）设计点的两种情况。为了突出程序的适用性并展示其性能，