Nonparametric Detection of Multiple Location-Scale Change Points via Wild Binary Segmentation

TL;DR

The paper introduces WBS-Lepage, a nonparametric method combining wild binary segmentation with a rank-based statistic to detect multiple location and scale change points without assuming a specific data distribution.

Contribution

It proposes a novel nonparametric change point detection method that is distribution-free and effective for both location and scale shifts, with an accompanying R package.

Findings

Performs well for detecting location changes.

Highly effective for detecting scale changes.

Provides finite-sample thresholds via Monte Carlo simulation.

Abstract

Change point methods are used to divide a sequence of observations into segments with different behaviour. Often, the distributional form of the observations is unknown, but the changes of interest are likely to involve shifts in location, scale, or both. We consider the problem of detecting multiple change points in a sequence without specifying a parametric model for the data. We propose the WBS-Lepage procedure, a nonparametric method which combines wild binary segmentation with a rank-based Lepage statistic. The statistic is formed from Mann--Whitney and Mood components, which are respectively sensitive to changes in location and scale. Since it depends on the observations only through their ranks, its null distribution is distribution-free. This allows finite-sample thresholds to be calibrated by Monte Carlo simulation, providing direct control over the probability of falsely detecting change points when none exist. We compare WBS-Lepage with existing nonparametric change point methods, including penalised likelihood and binary-segmentation-based competitors. The proposed method performs competitively for location changes and is particularly effective for detecting changes in scale. We illustrate the procedure on a stylometric analysis of changes in an author's writing style and provide an implementation of our method in the accompanying R package npwbs.