论文标题
相互作用的足够尺寸
Sufficient Dimension Reduction for Interactions
论文作者
论文摘要
降低尺寸是许多统计方法的核心。在回归中，缩小尺寸与充分性概念有关，在这种概念中，响应与一组预测变量的关系由预测变空间中的较低维子空间解释。在本文中，我们考虑了在子空间上的回归减小的概念，该子空间足以解释预测变量与另一个感兴趣的变量之间的相互作用效应。这项工作的动机来自精确医学，在鉴于一组预处理预测指标的情况下，个性化治疗规则的性能取决于相互作用的效果。
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower dimensional subspace in the predictor space. In this paper, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between predictors and another variable of interest. The motivation for this work is from precision medicine where the performance of an individualized treatment rule, given a set of pretreatment predictors, is determined by interaction effects.
