Narrowest Significance Pursuit: inference for multiple change-points in linear models

We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localised regions in data sequences which each must contain a change-point (understood as an abrupt change in the parameters of an underlying linear model), at a prescribed global significance level. NSP works with a wide range of distributional assumptions on the errors, and guarantees important stochastic bounds which directly yield exact desired coverage probabilities, regardless of the form or number of the regressors. In contrast to the widely studied “post-selection inference” approach, NSP paves the way for the concept of “post-inference selection”. An implementation is available in the R package nsp.

我们提出了最窄显著性追踪法（Narrowest Significance Pursuit，NSP），这是一种通用且灵活的方法论，可在指定的全局显著性水平下，自动检测数据序列中的局部区域——每个此类区域均需包含一个变点（即所基于的线性模型参数发生的突变）。该方法可适配多种误差项分布假设，并可保证重要的随机界，该随机界可直接导出精确的期望覆盖概率，且不受回归因子的形式与数量限制。相较于广受研究的“选后推断”方法，NSP为“推断后选择”这一概念铺平了道路。该方法的实现代码可在R语言包nsp中获取。