Status | Confirmed |
Seminar Series | SAMM |
Subjects | cond-mat.stat-mech,math.PR,math.ST |
Date | Friday 19 May 2017 |
Time | 11:30 |
Institute | SAMM |
Seminar Room | C20.13, Centre Pierre Mendès-France, Univ. Paris-1, 90 rue de Tolbiac, Paris |
Speaker's Last Name | Duval |
Speaker's First Name | Céline |
Speaker's Email Address | |
Speaker's Institution | MAP5 - Univ. Paris Descartes |
Title | Compound Poisson approximation to estimate the Lévy density |
Abstract | We construct an estimator of the Lévy density, with respect to the Lebesgue measure, of a pure jump Lévy process from high frequency observations. The main novelty of our result is that we directly estimate the Lévy density in cases where the process may present infinite activity. Moreover, we study the risk of the estimator with respect to $L_p$ loss functions, $1\leq p < \infty$ The main idea behind the estimation procedure that we propose is to use that "every infinitely divisible distribution is the limit of a sequence of compound Poisson distributions" and to take advantage of the fact that it is well known how to estimate the Lévy density of a compound Poisson process in the high frequency setting. We consider linear wavelet estimators and the performance of our procedure is studied in term of L_p loss functions. The results are illustrated with several examples. |
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