Narrowest Significance Pursuit: inference for multiple change-points in linear models

TL;DR

Narrowest Significance Pursuit (NSP) is a flexible method for detecting change-points in linear models with guaranteed coverage, applicable under various error distributions, and introduces the concept of post-inference selection.

Contribution

NSP provides a novel, distribution-agnostic approach for change-point detection with exact coverage guarantees, advancing beyond traditional post-selection inference methods.

Findings

Guarantees exact coverage probabilities for change-point detection.

Works under a wide range of error distribution assumptions.

Implemented in the R package nsp for practical use.

Abstract

We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localised regions in data sequences which each must contain a change-point (understood as an abrupt change in the parameters of an underlying linear model), at a prescribed global significance level. NSP works with a wide range of distributional assumptions on the errors, and guarantees important stochastic bounds which directly yield exact desired coverage probabilities, regardless of the form or number of the regressors. In contrast to the widely studied "post-selection inference" approach, NSP paves the way for the concept of "post-inference selection". An implementation is available in the R package nsp (see https://CRAN.R-project.org/package=nsp ).