聚类与弱相依数据下U统计量的极限理论
Limit Theory for U-Statistics under Clustered and Weakly Dependent Data
AI总结：
本文针对聚类与弱相依数据下的无界核k阶U统计量，建立渐近理论与可行推断方法，通过垂直重排分离关键项，证明相关估计量一致，扩展了U统计量的极限理论适用范围。
AI中文摘要：
本文针对聚类抽样和弱相依时间序列抽样下的无界核k阶U统计量，建立渐近理论与可行推断方法。分析首先构建完整的2阶流程，从聚类数据过渡到精确m相依，再到近epoch相依，随后将该逻辑扩展至k≥2的一般阶。在聚类抽样下，理论允许任意簇内相依及增长的非均衡簇大小；在弱相依下，基于独立同分布的近似序列将精确m理论推广至近epoch相依过程。核心组合工具是垂直重排，其将一阶Hoeffding投影（分析对象）与碰撞项、高阶退化余项（需显式控制）分离。结果表明，用于可行推断的一阶投影协方差的聚类稳健估计量与HAC估计量均具有一致性。
英文摘要：
This paper develops asymptotic theory and feasible inference for unbounded-kernel order-k U-statistics under clustered sampling and weakly dependent time-series. The analysis first builds the complete order-2 pipeline, moving from clustered data to exact $m$-dependence and then to near-epoch dependence. The same logic is subsequently extended to general order k greater or equal to 2. Under clustered sampling, the theory allows arbitrary within-cluster dependence and growing, unbalanced cluster sizes. Under weak dependence, an i.i.d.-based approximating sequence carries the exact-m theory to near-epoch-dependent processes. The common combinatorial device partitions the sample into columns, separating sampling-generic tuples, where the first-order Hoeffding projection is analysed, from collision terms and higher-order Hoeffding projection remainders, which are controlled explicitly. Cluster-robust and HAC estimators of the covariance of the first-order projection, needed for feasible inference, are shown to be consistent. Empirical applications and data-calibrated simulations for inequality, L-moment, and rank-dependence statistics illustrate the finite-sample performance of the proposed procedures.
