我们提出了一种全新、通用且灵活的非参数函数估计方法，该方法首先估计函数中可能存在的任意特征的数量和位置，随后在每对相邻的已检测特征之间以参数化方式估计函数。我们的方法可处理的特征示例包括分段常数信号模型中的变化点、分段线性信号模型中的折点，以及其他类似的不规则性，我们也将这些称为广义变化点。\n 我们的方法仅需稍作修改即可应用于一系列广义变化点场景，而我们之所以能实现如此高的通用性，是因为我们提出并使用了一种新型的多广义变化点检测工具，名为Narrowest-Over-Threshold（NOT，阈值最窄检测）。NOT的核心要素是其聚焦于数据中被怀疑存在特征的最小局部区段。至关重要的是，这种自适应定位技术可避免NOT考虑包含两个或更多特征的子样本，这是确保NOT普遍适用性的关键因素。\n 针对选定的场景，我们证明了NOT在检测广义变化点的数量和位置方面具有一致性和近似最优性。此外，我们提出通过强化施瓦茨信息准则（strengthened Schwarz Information Criterion, sSIC）（自动）选择NOT的阈值，并给出了理论依据。NOT估计量易于实现且计算速度快：整个阈值索引的解路径可在接近线性的时间内计算完成。重要的是，NOT方法便于用户根据自身需求进行扩展。目前没有单一的可比方法，但我们表明，在测试的场景中，NOT的性能与现有最优水平相当或更优。我们的方法已在R包not中实现。
英文摘要：
We propose a new, generic and flexible methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function, and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change-points in the piecewise-constant signal model, kinks in the piecewise-linear signal model, and other similar irregularities, which we also refer to as generalised change-points.
Our methodology works with only minor modifications across a range of generalised change-point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalised change-point detection device, termed Narrowest-Over-Threshold (NOT). The key ingredient of NOT is its focus on the smallest local sections of the data on which the existence of a feature is suspected. Crucially, this adaptive localisation technique prevents NOT from considering subsamples containing two or more features, a key factor that ensures the general applicability of NOT.
For selected scenarios, we show the consistency and near-optimality of NOT in detecting the number and locations of generalised change-points. Furthermore, we propose to select NOT's threshold (automatically) via the strengthened Schwarz Information Criterion (sSIC) and give theoretical justifications. The NOT estimators are easy to implement and rapid to compute: the entire threshold-indexed solution path can be computed in close-to-linear time. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. There is no single competitor, but we show that the performance of NOT matches or surpasses the state of the art in the scenarios tested. Our methodology is implemented in the R package \textbf{not}.
Frequent or Systematic Changes? discussion on "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection."
Genetic algorithm with a Bayesian approach for the detection of multiple points of change of time series of counting exceedances of specific thresholds
