There are many research works and methods about change point detection in the literature. However, there are only a few that provide inference for such change points after being estimated. This work mainly focuses on a statistical analysis of change points estimated by the PRUTF algorithm, which incorporates trend filtering to determine change points in piecewise polynomial signals. This paper develops a methodology to perform statistical inference, such as computing p-values and constructing confidence intervals in the newly developed post-selection inference framework. Our work concerns both cases of known and unknown error variance. As pointed out in the post-selection inference literature, the length of such confidence intervals are undesirably long. To resolve this shortcoming, we also provide two novel strategies, global post-detection, and local post-detection which are based on the intrinsic properties of change points. We run our proposed methods on real as well as simulated data to evaluate their performances.

翻译：文献中有许多关于变化点探测的研究工作和方法。然而,只有少数研究工作和方法在估算出这些变化点之后提供推断。这项工作主要侧重于对PRUTF算法估计的变化点进行统计分析,该算法包含趋势过滤,以确定片断多球信号的变化点。本文开发了一种统计推论方法,如计算P值和在新开发的选举后推断框架中建立信任间隔。我们的工作涉及已知和未知的错误差异。正如选后推论文献所指出的,这种信任间隔的长度是极长的。为了解决这一缺陷,我们还根据变化点的内在特性,提供了两个新的战略,即全球检测后检测和地方检测后检测战略。我们用真实和模拟数据来评估其性能。