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Asymptotic properties of intensity estimators for Poisson shot-noise processes

Published online by Cambridge University Press:  14 July 2016

Friedrich Liese  and
Volker Schmidt
Friedrich Liese*
Affiliation:
University of Rostock
Volker Schmidt*
Affiliation:
Mining Academy of Freiberg
*
∗ Postal address: Universität Rostock, Fachbereich Mathematik, Universitätsplatz 1, Rostock, D-02500, Germany.
∗∗ Postal address: Bergakademie Freiberg, Fachbereich Mathematik, Bernhard-von-Cotta-Str. 2, Freiberg, D-09200, Germany.
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Abstract

Stochastic processes {X(t)} of the form X(t) = Σ n f(t – Tn) are considered, where {Tn} is a stationary Poisson point process with intensity λ and f: R → R is an unknown response function. Conditions are obtained for weak consistency and asymptotic normality of estimators of λ based on long-run observations of {X(t)}.

Keywords

MOMENT METHODEMPIRICAL COVARIANCE FUNCTIONCONSISTENCYCONVERGENCE RATECENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 568 - 583
Copyright
Copyright © Applied Probability Trust 1991 

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