Dimension reduction for conditional mean in regression
Dimension reduction for conditional mean in regression
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DOI：
10.1214/aos/1021379861
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发表时间：
2002-04-01
影响因子：
4.5
通讯作者：
Bing, L
中科院分区：
文献类型：
--
作者：
Cook, RD;Bing, L
在许多情况下，回归分析主要关注推断给定预测变量的响应的条件均值，而不关心条件分布的其他方面。在本文中，我们开发了考虑到这一点的降维方法。我们引入了中心平均子空间（CMS）的概念，这是当对平均函数感兴趣时用于降维的自然推理对象。我们研究 CMS 的特性，并开发估计它的方法。这些方法包括一类新的估计器，它需要的条件比 pHd 少，并且当 pHd 的一个条件被违反时，它显示出明显的优势。 CMS 还揭示了现有降维方法之间的明显区别：OLS、pHd、SIR 和 SAVE。我们将新方法应用于涉及卧牛的数据集。
In many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors, and less concerned with the other aspects of the conditional distribution. In this paper we develop dimension reduction methods that incorporate this consideration. We introduce the notion of the Central Mean Subspace (CMS), a natural inferential object for dimension reduction when the mean function is of interest. We study properties of the CMS, and develop methods to estimate it. These methods include a new class of estimators which requires fewer conditions than pHd, and which displays a clear advantage when one of the conditions for pHd is violated. CMS also reveals a transparent distinction among the existing methods for dimension reduction: OLS, pHd, SIR and SAVE. We apply the new methods to a data set involving recumbent cows.