Ridge-regularized Hotelling-type (RHT) change-point tests depend on a ridge parameter $λ$, but the power-optimal value is determined by the unknown covariance structure and the unknown mean shift. We avoid selecting a single ridge value by computing fixed-ridge p-values on a finite deterministic grid and aggregating them with the Cauchy combination rule. Under the standard random-matrix conditions for fixed-ridge RHT statistics, we establish finite-grid joint weak convergence of the ridge processes. This leads to fixed-level validity under joint-limit calibration and small-tail validity for the analytic Cauchy p-value. Monte Carlo experiments show that deterministic-grid Cauchy aggregation has stable size behavior and achieves power close to the best stable fixed ridge choice across a range of covariance and signal configurations.

翻译：岭正则化霍特林型（RHT）变点检验依赖于岭参数 $λ$，但最优检验功效对应的参数值由未知的协方差结构和均值偏移共同决定。我们通过在有限确定性网格上计算固定岭的p值，并采用柯西组合规则对其进行聚合，从而避免了单一岭参数的选择问题。在固定岭RHT统计量的标准随机矩阵条件下，我们建立了岭过程在有限网格上的联合弱收敛性。这保证了联合极限校准下的固定水平有效性，以及解析柯西p值的小尾部有效性。蒙特卡洛实验表明，确定性网格的柯西聚合方法在不同协方差结构和信号配置下均保持稳定的尺寸表现，其检验功效接近最优稳定固定岭选择的结果。