Adaptive confidence bands for Markov chains and diffusions

Estimating the invariant measure and the drift

Journal Article (2016)
Author(s)

J. Söhl (University of Cambridge)

Mathias Trabs (Hamburg University of Technology)

Affiliation
External organisation
DOI related publication
https://doi.org/10.1051/ps/2016017
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Publication Year
2016
Language
English
Affiliation
External organisation
Volume number
20
Pages (from-to)
432-462

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.

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