Principal Fitted Components for Dimension Reduction in Regression
Principal Fitted Components for Dimension Reduction in Regression
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DOI：
10.1214/08-sts275
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发表时间：
2008-11-01
影响因子：
5.7
通讯作者：
Forzani, Liliana
中科院分区：
文献类型：
--
作者：
Cook, R. Dennis;Forzani, Liliana
我们针对在回归中困扰主成分使用的两个问题提供了补救措施：(I)主成分仅由预报器计算，并且没有明显地利用响应；(Ii)主成分在预报器的满秩线性变换下不是不变的或等变的。这一发展始于主要拟合成分[Cook，R.D.(2007)。费雪讲座：回归中的降维(带讨论)。统计学家。SCI。22 1-26]，并使用正态模型对响应上的预测者进行逆回归，以获得感兴趣的正向回归的还原信息。这种方法包括测试关于组件数量和预测者之间的条件独立性的假设的方法。
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression (with discussion). Statist. Sci. 22 1-26] and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among the predictors.