Abstract–Many well-known sufficient dimension reduction methods investigate the inverse conditional moments of the predictors given the response. The required linearity condition, the number and arrangement of slices, and the inability to detect symmetric dependence are among several long-standing issues that have negatively impacted on the use of these approaches. Motivated by two recent works dealing with the choice of number of slices, we propose a novel and effective method based on the aggregation of inverse mean estimation. The new approach can substantially improve the estimation accuracy, break down the symmetry to achieve exhaustive estimation, and is much less sensitive to the violation of the linearity condition. Both simulation studies and a real data application show the efficacy of the newly proposed approach.

摘要-许多众所周知的充分降维方法研究给定响应的预测变量的逆条件矩。所需的线性条件、切片的数量和排列以及无法检测对称依赖性是对这些方法的使用产生负面影响的几个长期存在的问题。受最近两篇涉及切片数量选择的作品的启发，我们提出了一种基于逆均值估计聚合的新颖有效的方法。新方法可以显着提高估计精度，打破对称性以实现详尽估计，并且对违反线性条件的敏感度要低得多。模拟研究和实际数据应用都显示了新提出的方法的有效性。