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Second order asymptotical efficiency for a Poisson process

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Abstract

We consider the problem of the non-parametric estimation of the mean function of an inhomogeneous Poisson process when its intensity function is periodic. For integral-type quadratic loss functions there is a classical lower bound for all estimators and the empirical mean function attains that lower bound, thus it is asymptotically efficient. Following the ideas of the work by Golubev and Levit, we compare asymptotically efficient estimators and propose an estimator which is second order asymptotically efficient. Second order efficiency is done over Sobolev ellipsoids, following the ideas of Pinsker.

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Authors and Affiliations

  1. Université du Maine, Le Mans, France

    S. B. Gasparyan

  2. Yerevan State University, Yerevan, Armenia

    S. B. Gasparyan

Authors
  1. S. B. Gasparyan
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Correspondence to S. B. Gasparyan.

Additional information

Original Russian Text © S. B. Gasparyan, 2015, published in Izvestiya NAN Armenii. Matematika, 2015, No. 2, pp. 13–23.

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Gasparyan, S.B. Second order asymptotical efficiency for a Poisson process. J. Contemp. Mathemat. Anal. 50, 98–106 (2015). https://doi.org/10.3103/S1068362315020065

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  • DOI: https://doi.org/10.3103/S1068362315020065

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