Functional estimation for Lévy measures of semimartingales with Poissonian jumps

Yasutaka Shimizu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1073-1092
Number of pages20
JournalJournal of Multivariate Analysis
Issue number6
Publication statusPublished - 2009 Jul
Externally publishedYes


  • 62G07
  • 62G20
  • 62M09
  • Asymptotic efficiency
  • Discrete observations
  • Functional estimation
  • Lévy measure
  • Semimartingales with jumps
  • primary
  • secondary

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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