Sliced regression for dimension reduction
Sliced regression for dimension reduction
复制标题
用于降维的切片回归
DOI：
10.1198/016214508000000418
复制
发表时间：
2008-06-01
影响因子：
3.7
通讯作者：
Xia, Yingcun
中科院分区：
文献类型：
--
作者：
Wang, Hansheng;Xia, Yingcun
提出了一种新的降维方法，包括对响应区域进行切片并对每个切片应用局部核回归。与传统的逆回归方法[例如切片逆回归（SIR）]相比，新方法不受线性条件的影响，具有更好的估计精度。与直接估计方法（例如MAVE）相比，新方法对极值具有更强的鲁棒性，并且可以详尽地捕获整个中心子空间（CS）。为了确定 CS 维度，开发了一致的交叉验证标准。广泛的数值研究，包括一个真实的例子，证实了我们的理论发现。
A new dimension-reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed. Compared with the traditional inverse regression methods [e.g., sliced inverse regression (SIR)], the new method is free of the linearity condition and has much better estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire central subspace (CS) exhaustively. To determine the CS dimension, a consistent cross-validation criterion is developed. Extensive numerical studies, including a real example, confirm our theoretical findings.