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There are many research works and methods about change point detection in theliterature. However, there are only a few that provide inference for suchchange points after being estimated. This work mainly focuses on a statisticalanalysis of change points estimated by the PRUTF algorithm, which incorporatestrend filtering to determine change points in piecewise polynomial signals.This paper develops a methodology to perform statistical inference, such ascomputing p-values and constructing confidence intervals in the newly developedpost-selection inference framework. Our work concerns both cases of known andunknown error variance. As pointed out in the post-selection inferenceliterature, the length of such confidence intervals are undesirably long. Toresolve this shortcoming, we also provide two novel strategies, globalpost-detection, and local post-detection which are based on the intrinsicproperties of change points. We run our proposed methods on real as well assimulated data to evaluate their performances.

Valid Post-Detection Inference for Change Points Identified Using Trend Filtering