Title: Fast and optimal inference for change points in piecewise polynomials via differencing Authors:  Shakeel Gavioli-Akilagun - London School of Economics (United Kingdom) [presenting]
Piotr Fryzlewicz - London School of Economics (United Kingdom)
Abstract: The problem of uncertainty quantification in change point regressions is considered, where the signal can be piecewise polynomial of arbitrary but fixed degree. Disjoint intervals are sought, which, uniformly at a given confidence level, must each contain a change point location. A procedure is proposed based on performing local tests at a number of scales and locations on a sparse grid, which adapts to the choice of the grid in the sense that by choosing a sparser grid, one explicitly pays a lower price for multiple testing. The procedure is fast as its computational complexity is always of the order $O(n\log(n))$ where $n$ is the length of the data, and optimal in the sense that under certain mild conditions, every change point is detected with high probability and the widths of the intervals returned match the mini-max localization rates for the associated change point problem up to log factors. A detailed simulation study shows that the procedure is competitive against state-of-the-art algorithms for similar problems. The procedure is implemented in the R package ChangePointInference, which is available via GitHub.