Adaptive drift estimation for nonparametric diffusion model

Vladimir G. Spokoiny

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.

Original languageEnglish
Pages (from-to)815-836
Number of pages22
JournalAnnals of Statistics
Volume28
Issue number3
DOIs
Publication statusPublished - 2000
Externally publishedYes

Keywords

  • Bandwidth selection
  • Drift and diffusion coefficients
  • Nonparametric estimation

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