For robust and efficient detection of change points, we introduce a novel methodology MUSCLE (multiscale quantile segmentation controlling local error) that partitions serial data into multiple segments, each sharing a common quantile. It leverages multiple tests for quantile changes over different scales and locations, and variational estimation. Unlike the often adopted global error control, MUSCLE focuses on local errors defined on individual segments, significantly improving detection power in finding change points. Meanwhile, due to the built-in model complexity penalty, it enjoys the finite sample guarantee that its false discovery rate (or the expected proportion of falsely detected change points) is upper bounded by its unique tuning parameter. Further, we obtain the consistency and the localisation error rates in estimating change points, under mild signal-to-noise-ratio conditions. Both match (up to log factors) the minimax optimality results in the Gaussian setup. All theories hold under the only distributional assumption of serial independence. Incorporating the wavelet tree data structure, we develop an efficient dynamic programming algorithm for computing MUSCLE. Extensive simulations as well as real data applications in electrophysiology and geophysics demonstrate its competitiveness and effectiveness. An implementation via R package muscle is available from GitHub.

翻译：为稳健高效地检测变点，我们提出一种新颖方法 MUSCLE（多尺度分位数分割局部误差控制），该方法将序列数据划分为多个共享同一分位数的分段。它利用多尺度、多位置的分位数变化多重检验及变分估计。与常采用的全局误差控制不同，MUSCLE 聚焦于定义在单个分段上的局部误差，显著提升了发现变点的检测能力。同时，由于内置的模型复杂度惩罚，它享有有限样本保证：其错误发现率（或错误检测变点的期望比例）受其唯一调优参数的上界约束。进一步地，在温和的信噪比条件下，我们得到了变点估计的一致性及定位误差率。两者（忽略对数因子）均匹配高斯设定下的极小极大最优性结果。所有理论仅在序列独立性这一分布假设下成立。结合小波树数据结构，我们开发了一种高效计算 MUSCLE 的动态规划算法。大量模拟实验以及电生理学和地球物理学中的真实数据应用证明了其竞争力和有效性。可通过 GitHub 获取 R 包 muscle 的实现。