Abstract

The aim of study is to show that the minimum distance estimator is consistent and asymptotically normal with the usual $\root \of n$ rate of convergence for the intensty function of the process Poisson which have a particularty form. We consider the problem of estimation of a multi-dimensional parameter $θ_o \>= \>(ω_1^o,\,...\,, \,ω_d^o,\,γ_1^o,\,...\,, \,γ_d^o)$. We suppose that the unknown parameter is 2d dimensional and the intensity function of the process is smooth the first d components and discontinuous the others d components of this parameter.

Keywords:

Asymptotic normality, non regular model minimum distance estimation, parameter estimation, poisson processes,

References

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.