Narrowest-over-threshold detection of multiple change points and change-point-like features
Narrowest-over-threshold detection of multiple change points and change-point-like features
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DOI：
10.1111/rssb.12322
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发表时间：
2019-07-01
影响因子：
5.8
通讯作者：
Fryzlewicz, Piotr
中科院分区：
文献类型：
--
作者：
Baranowski, Rafal;Chen, Yining;Fryzlewicz, Piotr
我们提出了一种新的、通用且灵活的非参数函数估计方法，其中我们首先估计函数中可能存在的任何特征的数量和位置，然后在每对相邻检测到的特征之间参数估计函数。我们的方法处理的特征示例包括分段恒定信号模型中的变化点、分段线性信号模型中的扭结以及其他类似的不规则性，我们也将其称为广义变化点。我们的方法只需对一系列广义变化点场景进行少量修改即可工作，并且我们通过提出和使用一种新的多广义变化点检测设备（称为最窄阈值以上（NOT）检测）来实现如此高度的通用性。 NOT 方法的关键要素是它关注怀疑存在特征的数据的最小局部部分。对于选定的场景，我们展示了 NOT 算法在检测广义变化点的数量和位置方面的一致性和接近最优性。 NOT 估计器易于实现且计算速度快。重要的是，NOT 方法很容易被用户扩展以适应自己的需求。我们的方法不是在 R 包中实现的。
We propose a new, generic and flexible methodology for non-parametric 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 generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.