Multi-purpose open-end monitoring procedures for multivariate observations based on the empirical distribution function

TL;DR

This paper introduces nonparametric open-end sequential tests for detecting any distributional change in multivariate data, with proven asymptotic properties and demonstrated finite-sample effectiveness.

Contribution

It develops new open-end monitoring procedures for multivariate observations based on the empirical distribution function, extending change detection capabilities.

Findings

Procedures effectively detect all types of distributional changes.

Asymptotic properties are rigorously established.

Good finite-sample performance shown through Monte Carlo simulations.

Abstract

We propose nonparametric open-end sequential testing procedures that can detect all types of changes in the contemporary distribution function of possibly multivariate observations. Their asymptotic properties are theoretically investigated under stationarity and under alternatives to stationarity. Monte Carlo experiments reveal their good finite-sample behavior in the case of continuous univariate, bivariate and trivariate observations. A short data example concludes the work.