We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging classical max-type and sum-type tests. We establish joint weak convergence of the extreme-value component and standardized $L$-statistics under mild conditions, yielding an asymptotic independence that justifies combining multiple $k$'s. An adaptive omnibus test is constructed via a Cauchy combination over a dyadic grid of $k$, and a wild bootstrap calibration is provided with theoretical guarantees. Simulations demonstrate accurate size and strong power across sparse and dense alternatives, including non-Gaussian designs.

翻译：本文提出了一种统一的高维回归系数$L$统计量检验框架，能够自适应于未知的稀疏性。所提出的统计量对坐标方向的证据度量进行排序，并聚合前$k$个信号，从而桥接了经典的极大值型检验与求和型检验。我们在温和条件下建立了极值分量与标准化$L$统计量的联合弱收敛性，得到了渐近独立性，这为组合多个$k$值提供了理论依据。通过在一个$k$的二进制网格上进行柯西组合，构建了一种自适应综合检验，并提供了具有理论保证的野自助法校准。模拟实验表明，该方法在稀疏与稠密备择假设（包括非高斯设计）下均能保持准确的检验水平并具有较高的检验功效。