Estimation for the invariant law of an ergodic diffusion process based on high-frequency data

Research output: Contribution to journalArticle

Abstract

Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t n 0 < t n 1 < ... < t n n such that t n n →∞ and n Δ 1+p n → 0, where Δ n = max 1≤i≤n; {pipe}t n i - t n i-1{pipe}, with p ∈ (0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

Original languageEnglish
Pages (from-to)909-915
Number of pages7
JournalJournal of Nonparametric Statistics
Volume23
Issue number4
DOIs
Publication statusPublished - 2011 Dec 1
Externally publishedYes

Keywords

  • Asymptotic efficiency
  • Ergodic diffusion
  • Invariant law
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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