Nonparametric estimation and testing time-homogeneity for processes with independent increments

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Abstract

We consider a nonparametric estimation problem for the Lévy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an ℓ-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the Lévy measure. Our result is a fruit of the empirical process theory and the martingale theory.

Original languageEnglish
Pages (from-to)1043-1055
Number of pages13
JournalStochastic Processes and their Applications
Volume118
Issue number6
DOIs
Publication statusPublished - 2008 Jun 1

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Keywords

  • Change point problem
  • Empirical process
  • Lévy process
  • Martingale
  • Nonparametric estimation
  • Process with independent increments

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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