Adaptive nonparametric estimation for L茅vy processes observed at low frequency

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• 作者：Johanna Kappus
• 关键词：Lé ; vy process ; Nonparametric estimation ; Adaptive estimation ; Deconvolution ; Model selection
• 刊名：Stochastic Processes and their Applications
• 出版年：January, 2014
• 年：2014
• 卷：124
• 期：1
• 页码：730-758
• 全文大小：314 K

文摘

This article deals with adaptive nonparametric estimation for L茅vy processes observed at low frequency. For general linear functionals of the L茅vy measure, we construct kernel estimators, provide upper risk bounds and derive rates of convergence under regularity assumptions.

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.