Functional estimation for Levy measures of semimartingales with Poissonian jumps

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Shimizu, Yasutaka

关键词: Semimartingales with jumps;    Levy measure;    Functional estimation;    Discrete observations;    Asymptotic efficiency;   

DOI  :  10.1016/j.jmva.2008.10.006

来源: Elsevier

【 摘 要 】

We consider semimartingales with jumps that have finite Levy measures. The purpose of this article is to estimate integral-type functionals of the Levy 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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free