Functional estimation for Lévy measures of semimartingales with Poissonian jumps
Functional estimation for Lévy measures of semimartingales with Poissonian jumps
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DOI：
10.1016/j.jmva.2008.10.006
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发表时间：
2009-07
期刊：
影响因子：
--
通讯作者：
Y. Shimizu
中科院分区：
文献类型：
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作者：
Y. Shimizu
我们考虑具有有限lsamvy测度的跳跃半鞅。本文的目的是从离散观测估计lsamy测度的积分型泛函。我们提出了两种类型的估计量：核估计量和经验估计量，这两种估计量都是由基于连续观测的目标渐近有效估计量直接离散得到的。当样本容量趋于无穷且采样间隔趋于零时，我们给出了估计量在渐近极大极小意义下的渐近效率。
We consider semimartingales with jumps that have finite Lévy measures. The purpose of this article is to estimate integral-type functionals of the Lévy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by direct discretization from asymptotically efficient estimators of the target based on continuous observations. We show the asymptotic efficiency in the asymptotic minimax sense of our estimators as the sample size tends to infinity and the sampling interval tends to zero.