Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift

Jakob Söhl, Mathias Trabs

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

As a starting point we prove a functional central limit theorem for estimators of the invariant measure of a geometrically ergodic Harris-recurrent Markov chain in a multi-scale space. This allows to construct confidence bands for the invariant density with optimal (up to undersmoothing) L-diameter by using wavelet projection estimators. In addition our setting applies to the drift estimation of diffusions observed discretely with fixed observation distance. We prove a functional central limit theorem for estimators of the drift function and finally construct adaptive confidence bands for the drift by using a completely data-driven estimator.

Original languageEnglish
Pages (from-to)432-462
Number of pages31
JournalESAIM - Probability and Statistics
Volume20
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Adaptive confidence bands
  • Diffusion
  • Drift estimation
  • Ergodic Markov chain
  • Functional central limit theorem
  • Lepski's method
  • Stationary density

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