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Large deviation probabilities in estimation of Poisson random measures

Florens, Danielle; Pham, Huyen (1998), Large deviation probabilities in estimation of Poisson random measures, Stochastic Processes and their Applications, 76, 1, p. 117-139. http://dx.doi.org/10.1016/S0304-4149(98)00005-2

Type
Article accepté pour publication ou publié
Date
1998
Journal name
Stochastic Processes and their Applications
Volume
76
Number
1
Publisher
Elsevier
Pages
117-139
Publication identifier
Metadata
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Author(s)
Florens, Danielle
Pham, Huyen
Abstract (EN)
We consider the parametric estimation problem of intensity measure of a Poisson random measure. We prove large deviation principles for Poisson random measures and an implicit contraction principle. These results are applied to provide a large deviation principle for a maximum likelihood estimator in a parametric statistical model and to explicitly identify the rate function.
Subjects / Keywords
Large deviations; Poisson random measures; Maximum likelihood estimator