There is a great amount of work that stands to benefit from quantile regression (QR), especially when the extreme parts of data are of interest. Although QR has been well developed, it has recently received particular interest in the area of dimension reduction. Existing dimension reduction techniques for conditional quantiles focus on commonly used types of data, such as quantitative predictor variables without any time-dependent structure. However, in this work we show how partial dimension reduction techniques can be extended to conditional quantiles in order to facilitate analysing data involving both quantitative and categorical predictor variables and/or longitudinal data. Simulation examples and a real data application demonstrate the easy to implement algorithm and its good finite sample performance.

有大量工作可以从分位数回归 (QR) 中受益，尤其是在对数据的极端部分感兴趣时。尽管 QR 已经得到很好的发展，但它最近在降维领域受到了特别的关注。现有的条件分位数降维技术侧重于常用的数据类型，例如没有任何时间相关结构的定量预测变量。然而，在这项工作中，我们展示了如何将部分降维技术扩展到条件分位数，以便于分析涉及定量和分类预测变量和/或纵向数据的数据。仿真实例和实际数据应用证明了该算法易于实现及其良好的有限样本性能。