AI 中文总结
针对高频连续时间回归的超高维点支撑筛选问题，提出带路径Lepski自适应的部分残差点迭代筛选方法，通过理论推导与实验验证实现确定性筛选。
AI 中文摘要
我们研究高频连续时间回归的变量筛选问题，目标是点回归系数的支撑。在逐坐标截断和有限变差跳跃条件下，我们建立了边际相关向量和协变量相关矩阵的局部估计的逐元素一致界。在局部平均α-Hölder条件下，速率为{（log p）/n}^（α/(2α+1)）（对数因子除外），这为边际支撑提供了确定性筛选保证。我们还推导了列表大小极小极大下界，当保留列表大小d满足log(p/d)≍log p时，该下界与定位和多重性阶数匹配。针对局部依赖下的回归支撑恢复，我们提出了带路径Lepski自适应的部分残差点迭代筛选方法。在稀疏特征值和标准化beta-min条件下，该方法具有确定性筛选性质，且仅需当前活动集相关的协变量列。模拟研究和高频因子应用验证了其性能。
英文摘要
We study variable screening for high-frequency continuous-time regression, targeting the support of the spot regression coefficient. We establish uniform entrywise bounds for local estimates of the marginal correlation vector and covariate correlation matrix under coordinatewise truncation and finite-variation jumps. Under a local averaged $α$-Hölder condition, the rate is $\{(\log p)/n\}^{α/(2α+1)}$, up to logarithmic factors. This yields sure screening for the marginal support. We also derive a list-size minimax lower bound that matches the localization and multiplicity order when the retained list size $d$ satisfies $\log(p/d)\asymp\log p$. For regression-support recovery under local dependence, we propose partial-residual spot iterative screening with pathwise Lepski adaptation. Under sparse eigenvalues and standardized beta-min, the procedure has the sure screening property and requires only correlation columns associated with the current active set. Simulation studies and a high-frequency factor application illustrate its performance.
