Adaptive nonparametric estimation for Levy processes observed at low frequency

作者：Kappus Johanna^*

来源：Stochastic Processes and Their Applications, 2014, 124(1): 730-758.

DOI：10.1016/j.spa.2013.08.010

• Levy process
• Nonparametric estimation
• Adaptive estimation
• Deconvolution
• Model selection

This article deals with adaptive nonparametric estimation for Levy processes observed at low frequency. For general linear functionals of the Levy measure, we construct kernel estimators, provide upper risk bounds and derive rates of convergence under regularity assumptions. %26lt;br%26gt;Our focus lies on the adaptive choice of the bandwidth, using model selection techniques. We face here a non-standard problem of model selection with unknown variance. A new approach towards this problem is proposed, which also allows a straightforward generalization to a classical density deconvolution framework.

• 出版日期2014-1