Maximum likelihood estimator in a multi-phase random regression model

Abstract

We consider a random regression model with several-fold change-points. The results for one change-point are generalized. The maximum likelihood estimator of the parameters is shown to be consistent, and the asymptotic distribution for the estimators of the coefficients is shown to be Gaussian. The estimators of the change-points converge, with n ⁻¹ rate, to the vector whose components are the left end points of the maximizing interval with respect to each change-point. The likelihood process is asymptotically equivalent to the sum of independent compound Poisson processes.

Keywords:

• multiple change-points
• parametric regression
• maximum likelihood estimator
• asymptotic properties

2000 Mathematics Subject Classifications :

• 62F12
• 62J02
• 62F10
• 60J75

Acknowledgements

The authors are grateful to the two referees whose comments and suggestions were valuable to improve the exposition of the paper.