  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.

Methodology