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- Title
Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes.
- Authors
Comte, Fabienne; Genon-Catalot, Valentine
- Abstract
In this paper, we study non-parametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations that may be irregularly sampled or possibly corrupted by a small noise independent of the main process. The case of non-noisy observations with regular sampling interval has been studied by the authors in previous works which are the benchmark for the extensions proposed here. We study first the case of a regular sampling interval and noisy data, then the case of irregular sampling for non-noisy data. In each case, non adaptive and adaptive estimators are proposed and risk bounds are derived.
- Subjects
ESTIMATION theory; DISCRETE-time systems; STATISTICAL sampling; JUMP processes; LEVY processes
- Publication
Statistica Neerlandica, 2010, Vol 64, Issue 3, p290
- ISSN
0039-0402
- Publication type
Article
- DOI
10.1111/j.1467-9574.2010.00462.x