🤖 AI Summary
Classical variance change-point detection methods suffer from p-value bias and inflated Type I error due to data reuse in model selection. Existing post-selection inference (PSI) frameworks are restricted to mean-shift detection and do not extend to variance changes.
Method: This paper introduces the first PSI framework for variance change-point detection, proposing two general-purpose constructions for post-selection p-values compatible with diverse algorithms (e.g., piecewise constant modeling) and test forms (e.g., constrained likelihood ratio tests). Leveraging conditional inference, convex optimization, and statistical functional theory, the methods rigorously control Type I error conditional on the selected model path and yield uniformly calibrated p-values.
Contribution/Results: We establish theoretical validity of the proposed procedures and demonstrate, via extensive simulations and real-data analyses, their improved statistical power and accurate p-value calibration—overcoming a key limitation of PSI in detecting heteroscedastic structural changes.
📝 Abstract
Quantifying uncertainty in detected changepoints is an important problem. However it is challenging as the naive approach would use the data twice, first to detect the changes, and then to test them. This will bias the test, and can lead to anti-conservative p-values. One approach to avoid this is to use ideas from post-selection inference, which conditions on the information in the data used to choose which changes to test. As a result this produces valid p-values; that is, p-values that have a uniform distribution if there is no change. Currently such methods have been developed for detecting changes in mean only. This paper presents two approaches for constructing post-selection p-values for detecting changes in variance. These vary depending on the method use to detect the changes, but are general in terms of being applicable for a range of change-detection methods and a range of hypotheses that we may wish to test.