论文标题
高维变化的分位数回归模型的选择后推断
Post-selection inference on high-dimensional varying-coefficient quantile regression model
论文作者
论文摘要
分位数回归已成功用于研究异质和重尾数据。变化的模型通常用于捕获输入变量对响应的影响随索引或时间的函数的变化。在这项工作中，我们研究了高维变化的分位数回归模型，并开发了用于统计推断的新工具。我们专注于开发有效的置信区间和在固定时间点和分位数上对非参数系数的诚实测试，同时允许在输入变量数量超过样本量的高维设置。由于估计模型选择技术的使用情况，因此在此制度中执行统计推断是具有挑战性的。但是，我们可以开发有效的推论工具，这些工具适用于广泛的数据生成过程，并且不会遭受模型选择引入的偏见。我们进行了数值模拟以证明方法的有限样本性能，并且还用真实的数据示例说明了应用程序。
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.
