Functional estimation for Lvy measures of semimartingales with Poissonian jumps

Yasutaka Shimizu

Journal of Multivariate Analysis, 2009, vol. 100, issue 6, 1073-1092

Abstract: We consider semimartingales with jumps that have finite Lvy measures. The purpose of this article is to estimate integral-type functionals of the Lvy 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.

Keywords: primary; 62M09 secondary; 62G20; 62G07 Semimartingales with jumps Lvy measure Functional estimation Discrete observations Asymptotic efficiency (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (7)

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