Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities

By Patricia Reynaud-Bouret. 2003

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ecac983bd4b6e17eb5972d9666a7e6de73ee59cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Vincent Rivoirard
2. Y. Baraud
3. Patricia Reynaud-Bouret
4. Lucien Birgé
5. Bert Van Es
6. Peter Spreij
7. S. Gugushvili
8. Valentine Genon-Catalot

In Finance

1. Valentine Genon-Catalot
2. Fabienne Comte
3. Y. Baraud
4. Lucien Birgé
5. Vincent Rivoirard
6. Bert Van Es
7. Peter Spreij
8. S. Gugushvili

In Statistics and Probability

1. Patricia Reynaud-Bouret
2. Lucien Birgé
3. Vincent Rivoirard
4. Fabienne Comte
5. Valentine Genon-Catalot
6. Y. Baraud
7. Bert Van Es
8. Peter Spreij

Citations in the corpus

• Poisson inverse problems (2006, unknown): “αˆt,λ −hu j λ,Kfi 2 = ∑ |λ|<j 1 t Z uj λdG −hu j λ,Kfi 2 . 23 Noticing that χ(Sj) = sup {a∈Rjd;k(aλ)|λ|<jk2<1} Z ∑|λ|<j aλu j λ t (dG −tKfdµ), we can use Corollary 2 of Reynaud-Bouret [24] about concentration inequalities for Poisson processes to get, for any w > 0 and ǫ > 0, P n ”
• Estimating the intensity of a random measure by histogram type estimators (2006, methodology): “(17) This theorem should be compared with the results of Reynaud-Bouret [38] who uses more general families of projection estimators than just histograms based on partitions.”
• 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]).”
• Near optimal thresholding estimation of a Poisson intensity on the real line (2008, background): “ Besov ball and on Φ. When p≤ 2, the rate of the risk of f˜n,γ corresponds to the minimax rate (up to the logarithmic term) for estimation of a compactly supported intensity of a Poisson process (see [30]), or for estimation of a compactly supported density (see [18]). Roughly speaking, it means tha”
• A kernel type nonparametric density estimator for decompounding (2005, methodology): “Inspired by methods used for the nonparametric estimation of the intensity functions of Poisson point processes, a penalised projection estimator as proposed in [14] is suggested.”