Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or time. In this work, we study high-dimensional varying-coefficient quantile regression models and develop new tools for statistical inference. We focus on development of valid confidence intervals and honest tests for nonparametric coefficients at a fixed time point and quantile, while allowing for a high-dimensional setting where the number of input variables exceeds the sample size. Performing statistical inference in this regime is challenging due to the usage of model selection techniques in estimation. Nevertheless, we can develop valid inferential tools that are applicable to a wide range of data generating processes and do not suffer from biases introduced by model selection. We performed numerical simulations to demonstrate the finite sample performance of our method, and we also illustrated the application with a real data example.
翻译:量性回归成功地用于研究多种和重尾数据。 差异性系数模型经常用来捕捉输入变量对反应的影响变化的变化,作为指数或时间的函数。 在这项工作中,我们研究高维不同系数回归模型,并开发新的统计推理工具。我们侧重于在固定时间点和量点上开发有效的信任间隔和对非参数系数进行诚实测试,同时允许在输入变量数量超过抽样大小的高度设置。由于在估算中使用模型选择技术,在这个制度中进行统计推论具有挑战性。然而,我们可以开发适用于广泛数据生成过程的有效推论工具,而不受模型选择的偏差影响。我们进行了数字模拟,以展示我们方法的有限样本性能,我们还用一个真实的数据实例来演示了应用。