| Autor: |
Bigot, J��r��mie, Gadat, S��bastien, Klein, Thierry, Marteau, Cl��ment |
| Rok vydání: |
2011 |
| Předmět: |
|
| DOI: |
10.48550/arxiv.1105.3625 |
| Popis: |
This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show that estimating this intensity is a deconvolution problem for which the density of the random shifts plays the role of the convolution operator. In an asymptotic setting where the number n of observed trajectories tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Besov balls. Non-linear thresholding in a Meyer wavelet basis is used to derive an adaptive estimator of the intensity. The proposed estimator is shown to achieve a near-minimax rate of convergence. This rate depends both on the smoothness of the intensity function and the density of the random shifts, which makes a connection between the classical deconvolution problem in nonparametric statistics and the estimation of a mean intensity from the observations of independent Poisson processes. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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