论文标题
多元边界回归模型
Multivariate boundary regression models
论文作者
论文摘要
在这项工作中，我们考虑了具有单方面错误的多元回归模型。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算，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。从以应用程序为导向的角度来看，对多元协变量的考虑为不可否认的机会提供了机会，但它需要一种新的证明方法来替换单变量案例已建立的证明。本文的主要目的是显示统一的一致性，并提供多变量随机协变量和多元确定性设计点的被考虑的非参数估计器的收敛速率。为了证明估计量的性能，在第二和第三维的模拟研究中研究了小样本行为。
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.
