Change point detection based on method of moment estimators

TL;DR

This paper introduces a change point detection method utilizing the method of moment estimators, establishing its theoretical properties and demonstrating its application to parametric models.

Contribution

It proposes a new change point detection procedure based on moment estimators with proven asymptotic behavior and consistency, including an estimator for the change point.

Findings

The test statistic's asymptotic distribution is derived under null and alternative hypotheses.

The proposed change point estimator is shown to be consistent.

Applications to parametric families demonstrate the method's effectiveness.

Abstract

A change point detection procedure using the method of moment estimators is proposed. The test statistics is based on a suitable $Z$-process. The asymptotic behavior of this process is established under both the null and the alternative hypothesis and the consistency of the test is also proved. An estimator for the change point is proposed and its consistency is derived. Some examples of this method applied to a parametric family of random variables are presented.