2021/04/24 by Reza Valiollahi Mehrizi, Mehrizi, Reza Valiollahi, Shojaeddin Chenouri +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Inference #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2104.12022
openalex publication_date 2021/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.