Change-Point Detection in Two-Phase Regression with Inequality Constraints on the Regression Parameters

Abstract

Two-phase regression models with inequality constraints on the regression coefficients and with a small number of measurements is considered. A new test based on the likelihood ratio in linear model with inequality constraints for the presence of a change-point is proposed. Numerical approximations to the powers against various alternatives are given and compared with the powers of the likelihood ratio test in the two-phase regression models without inequality constraints, the backwards CUSUM test, and the k-linear-r-ahead recursive residuals tests. Performance of related likelihood based estimators of the change-point is briefly studied in a Monte Carlo experiment.

Keywords:

• Change-point
• Likelihood based estimator
• Likelihood ratio test
• Linear regression model with inequality constraints
• Two-phase regression

Mathematics Subject Classification:

• 62F03
• 62F30
• 62J05

Acknowledgment

The author thanks Prof. Z. Szkutnik and the reviewers for helpful suggestions.