We propose Robust Narrowest Significance Pursuit (RNSP), a methodology for detecting localized regions in data sequences which each must contain a change-point in the median, at a prescribed global significance level. RNSP works by fitting the postulated constant model over many regions of the data using a new sign-multiresolution sup-norm-type loss, and greedily identifying the shortest intervals on which the constancy is significantly violated. By working with the signs of the data around fitted model candidates, RNSP fulfils its coverage promises under minimal assumptions, requiring only sign-symmetry and serial independence of the signs of the true residuals. In particular, it permits their heterogeneity and arbitrarily heavy tails. The intervals of significance returned by RNSP have a finite-sample character, are unconditional in nature and do not rely on any assumptions on the true signal. Code implementing RNSP is available at https://github.com/pfryz/nsp.

翻译：我们提出鲁棒最窄显著性追踪（Robust Narrowest Significance Pursuit, RNSP），该方法可在预设全局显著性水平下，检测数据序列中每个必须包含中位数变点的局部区域。RNSP通过采用新型符号多分辨率上确界范数型损失函数，在数据多个区域拟合假设的常数模型，并贪婪地识别常数性被显著违反的最短区间。通过利用数据围绕拟合模型候选的符号信息，RNSP仅需真实残差符号的符号对称性与序列独立性这一最弱假设即可保证覆盖承诺，尤其允许残差异方差性及任意重尾分布。RNSP返回的显著性区间具有有限样本特征，本质上是无条件的，且不依赖真实信号的任何假设。实现RNSP的代码已发布于 https://github.com/pfryz/nsp。