Nonparametric tests for change-point detection \`a la Gombay and Horv\'ath

TL;DR

This paper extends Gombay and Horvath's nonparametric change-point detection tests using empirical process theory, improving finite-sample performance and applying to multivariate data with practical recommendations.

Contribution

It generalizes the change-point detection tests to multivariate settings and enhances their finite-sample behavior using a sequential multiplier CLT approach.

Findings

Improved finite-sample performance of change-point tests

Effective application to multivariate hydrological data

Extensive Monte Carlo experiments demonstrating test performance

Abstract

The nonparametric test for change-point detection proposed by Gombay and Horv\'ath is revisited and extended in the broader setting of empirical process theory. The resulting testing procedure for potentially multivariate observations is based on a sequential generalization of the functional multiplier central limit theorem and on modifications of Gombay and Horv\'ath's seminal approach that appears to improve the finite-sample behavior of the tests. A large number of candidate test statistics based on processes indexed by lower-left orthants and half-spaces are considered and their performance is studied through extensive Monte Carlo experiments involving univariate, bivariate and trivariate data sets. Finally, practical recommendations are provided and the tests are illustrated on trivariate hydrological data.