Density-Based Empirical Likelihood Ratio Change Point Detection Policies

Abstract

Nonparametric detection of a change in distribution is studied when observations are independent. We provide a general method for constructing distribution-free change point detection schemes that have approximately likelihood structures. This method utilizes principles of the maximum empirical likelihood (EL) approach to approximate powerful parametric likelihood ratios. The product of the approximation can be associated with entropy-based test statistics. Entropy-based tests have been well addressed in the literature in the context of powerful decision rules for goodness of fit. We extend the entropy-based technique, using the EL principles. CUSUM and Shiryayev–Roberts (SR) detection policies are shown to be powerful parametric likelihood tests for detecting a change in distribution. We apply the proposed method to obtain nonparametric forms of the CUSUM and SR procedures. A Monte Carlo study demonstrates that the proposed method provides very efficient tests when comparing with the classical procedures. An example based on a real data is provided to demonstrate implementation and effectiveness of the new tests.

Keywords:

• Change point
• CUSUM
• Empirical likelihood
• Nonparametric tests
• Sample entropy
• Shiryayev–Roberts procedure

Mathematics Subject Classification:

• Primary 62G10, 62G30
• Secondary 62E17

Acknowledgments

We are grateful to anonymous referees for their helpful comments that clearly improved this article. This work was partially supported by the Internal Funding Program of the Shamoon College of Engineering (SCE).