On multiple change-point estimation for Poisson process

ABSTRACT

This work is devoted to the problem of change-point parameter estimation in the case of the presence of multiple changes in the intensity function of the Poisson process. It is supposed that the observations are independent inhomogeneous Poisson processes with the same intensity function and this intensity function has two jumps separated by a known quantity. The asymptotic behavior of the maximum-likelihood and Bayesian estimators are described. It is shown that these estimators are consistent, have different limit distributions, the moments converge and that the Bayesian estimators are asymptotically efficient. The numerical simulations illustrate the obtained results.

KEYWORDS:

• Bayesian estimator
• change-point
• inhomogeneous Poisson process
• likelihood ratio process
• maximum-likelihood estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F12
• 62F15
• 62M05
• 62N02

Funding

This work was performed under partial financial support of the grant of RSF [grant number 15-11-10022].