Nonparametric inference for discretely sampled Levy processes

作者：Gugushvili Shota^*

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2012, 48(1): 282-307.

DOI：10.1214/11-AIHP433

• Empirical characteristic function
• Empirical process
• Fourier inversion
• Levy density
• Levy process
• Maximal inequality
• Mean square error

Given a sample from a discretely observed Levy process X = (X-t)(t %26gt;= 0) of the finite jump activity, the problem of nonparametric estimation of the Levy density rho corresponding to the process X is studied. An estimator of rho is proposed that is based on a suitable inversion of the Levy-Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of rho over suitable classes of Levy triplets. The corresponding lower bounds are also discussed.

• 出版日期2012-2