Non asymptotic expansions of the MME in the case of Poisson observations

O. V. Chernoyarov, A. S. Dabye, F. N. Diop and Y. A. Kutoyants ()
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O. V. Chernoyarov: National Research University “MPEI”
A. S. Dabye: University Gaston Berger
F. N. Diop: University of Thies
Y. A. Kutoyants: National Research University “MPEI”

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 8, No 1, 927-950

Abstract: Abstract In this paper the problem of one dimensional parameter estimation is considered in the case where observations are coming from inhomogeneous Poisson processes. The method of moments estimation is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of the estimator and the expansion of the distribution function. The stochastic expansion, the expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are presented to illustrate the theoretical results.

Keywords: Poisson process; Parameter estimation; Method of moments; Expansion of estimators; Expansion of the moments; Expansion of distribution function; Non asymptotic expansions; 62M05; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00855-w

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