ABSTRACT

Quantile regression (QR) is a well-established method of tail analysis. Application of QR can become very challenging when dealing with high-dimensional data, thus requiring dimension reduction techniques. While the current literature on these techniques focuses on extracting linear combinations of the predictor variables that contain all the information about the conditional quantile, non-linear features can potentially achieve greater dimension reduction. We, therefore, present the first application of transformed dimension reduction for conditional quantiles, which serves as an intermediate step between linear and nonlinear dimension reduction. The idea is to transform the predictors monotonically and then look for low-dimensional projections by applying linear dimension reduction techniques. The performance of the proposed methodology is demonstrated through simulation examples and a real data application.

摘要

分位数回归 (QR) 是一种行之有效的尾部分析方法。在处理高维数据时，QR 的应用会变得非常具有挑战性，因此需要降维技术。虽然当前关于这些技术的文献侧重于提取包含有关条件分位数的所有信息的预测变量的线性组合，但非线性特征可以潜在地实现更大的降维。因此，我们提出了条件分位数的变换降维的第一个应用，它作为线性和非线性降维之间的中间步骤。想法是改造预测变量单调，然后通过应用线性降维技术寻找低维投影。所提出的方法的性能通过仿真示例和实际数据应用来证明。