Near optimal thresholding estimation of a Poisson intensity on the real line
By Patricia Reynaud-Bouret, Vincent Rivoirard. 2008
54 citations recorded by the source corpus.
The purpose of this paper is to estimate the intensity of a Poisson process N by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of N with respect to ndx where n is a fixed parameter, is assumed to be non-compactly supported. The estimator ˜ fn,γ based on random thresholds is proved to achieve the same performance as the oracle estimator up to a possible logarithmic term. Then, minimax properties of ˜ fn,γ on Besov spaces B α p,q are established. Under mild assumptions, we prove that
Subfields: Applied Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4932ac6c269f38c1fd4bbc4fa021b7747da57544
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In Applied Mathematics
In Finance
- Valentine Genon-Catalot
- Fabienne Comte
- Christian M. Hafner
- Helmut Herwartz
- Christian Francq
- Jean-Michel Zakoian
- Pentti Saikkonen
In Mathematical Physics
Citations in the corpus
- Adaptive Laguerre density estimation for mixed Poisson models (2015, background): “Kutoyants (1998) [16], chapter 6, and more recently, Reynaud (2003) [23], Reynaud and Rivoirard (2010) [24]).”