分位数回归的分布式选择性推断
Distributed Selective Inference for Quantile Regression
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- School of Mathematics and Statistics, Changchun University of Technology（长春工业大学数学与统计学院）
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中文总结 AI 辅助
针对高维分位数回归的后选择推断难题，提出仅需三轮通信的分布式选择性推断框架，通过响应替代策略处理非光滑分位数损失，经模拟与实际数据验证其有限样本性能良好。
中文摘要 AI 辅助
我们提出了一种针对高维分位数回归的分布式选择性推断框架。为了在该场景下实现有效的后选择推断，我们通过响应替代策略解决了非光滑分位数损失带来的计算挑战，该策略将问题转化为惩罚最小二乘形式，从而便于应用分布式选择性推断。为实现有效的后选择推断，我们引入了一种随机过程，其中Lasso选择事件通过关联的卡罗需-库恩-塔克（Karush-Kuhn-Tucker）条件表征，并在给定选择事件的情况下推导了聚合估计量的条件分布。所得算法仅需本地机器与中央服务器之间进行三轮通信。在标准正则条件下，我们证明了所提过程的渐近有效性，并开发了一种大偏差近似方法以用于选择性似然的计算可行实现。模拟研究和实际数据应用表明，所提方法具有令人满意的有限样本性能。
英文摘要
We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.
