Abstract

The model considered has two types of discontinuities. The first parameter is a parameter of scale; the second is a parameter of translation. The aim of study is to show that the minimum distance estimator is consistent and asymptotically normal. The problem of estimation studied in this work is the same time singular and regular. It is singular because the intensity is a discontinuous function and we obtains the consistency with the discontinuity and the study of asymptotic normality is based on the regularity of the function $Λ\,(􏰁θ, \:t)$.

Keywords:

Asymptotic properties, minimum distance estimator, parameter estimation, Poisson process, singular estimation,

References

Competing interests

The authors have no competing interests.

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The authors have no competing interests.