标题： 检验函数：覆盖中心子空间的新方法 显示英文标题

标题： Test function: A new approach for covering the central subspace

摘要： 本文提出了一种完整的充分降维方法，称为检验函数（TF）。 TF基于对响应变量的非线性变换，提供了一类新的估计中心子空间（CS）的方法。 与现有方法相比，TF的理论背景是在更弱的条件下发展起来的。 通过考虑预测变量关于响应变量的一阶和二阶条件矩，我们将TF分为两类。 在每一类中，我们给出了保证完全估计CS的条件。 此外，最优成员通过最小化由CS与其估计值之间的距离引起的渐近均方误差来计算。 这导致了两种嵌入式方法，并通过多个模拟进行了评估。 显示英文摘要

摘要： In this paper we offer a complete methodology for sufficient dimension reduction called the test function (TF). TF provides a new family of methods for the estimation of the central subspace (CS) based on the introduction of a nonlinear transformation of the response. Theoretical background of TF is developed under weaker conditions than the existing methods. By considering order 1 and 2 conditional moments of the predictor given the response, we divide TF in two classes. In each class we provide conditions that guarantee an exhaustive estimation of the CS. Besides, the optimal members are calculated via the minimization of the asymptotic mean squared error deriving from the distance between the CS and its estimate. This leads us to two plug-in methods which are evaluated with several simulations.