In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general Hölder class and estimate it via a nonparametric local polynomial approach that consists of minimization of the local integral of a polynomial approximation lying above the data points. While the consideration of multivariate covariates offers an undeniable opportunity from an application-oriented standpoint, it requires a new method of proof to replace the established ones for the univariate case. The main purpose of this paper is to show the uniform consistency and to provide the rates of convergence of the considered nonparametric estimator for both multivariate random covariates and multivariate deterministic design points. To demonstrate the performance of the estimators, the small sample behavior is investigated in a simulation study in dimension two and three.

中文翻译：

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多元边界回归模型

在这项工作中，我们考虑了一个具有单边误差的多元回归模型。我们假设回归函数位于一般的 Hölder 类中，并通过非参数局部多项式方法对其进行估计，该方法包括最小化位于数据点上方的多项式近似的局部积分。虽然从面向应用的角度来看，多元协变量的考虑提供了不可否认的机会，但它需要一种新的证明方法来代替单变量情况下已建立的证明方法。本文的主要目的是展示统一一致性，并为多元随机协变量和多元确定性设计点提供所考虑的非参数估计量的收敛率。为了证明估计器的性能，