标题： 利用加权卡方检验的切片逆矩回归降维方法 显示英文标题

标题： Sliced Inverse Moment Regression Using Weighted Chi-Squared Tests for Dimension Reduction

摘要： 我们提出了一种用于回归降维的新方法，该方法利用了前两个逆矩。 我们开发了相应的加权卡方检验来确定回归的维度。 所提出的方法考虑了切片逆回归（SIR）和一种使用新候选矩阵的方法的线性组合，这种新候选矩阵旨在恢复整个逆二阶矩子空间。 可以通过从维度检验中得出的p值来选择最佳组合。 理论上，所提出的方法以及切片平均方差估计（SAVE）比SIR和主Hessian方向（pHd）更能恢复完整的中心降维子空间。 因此，在理论层面上，它可以替代SIR、pHd、SAVE或它们的任意线性组合。 模拟研究表明，所提出的方法可能比SIR、pHd和SAVE具有更一致的功率。 显示英文摘要

摘要： We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of Sliced Inverse Regression (SIR) and the method using a new candidate matrix which is designed to recover the entire inverse second moment subspace. The optimal combination may be selected based on the p-values derived from the dimension tests. Theoretically, the proposed method, as well as Sliced Average Variance Estimate (SAVE), are more capable of recovering the complete central dimension reduction subspace than SIR and Principle Hessian Directions (pHd). Therefore it can substitute for SIR, pHd, SAVE, or any linear combination of them at a theoretical level. Simulation study indicates that the proposed method may have consistently greater power than SIR, pHd, and SAVE.