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 language | English |
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Pages (from-to) | 432-462 |
Number of pages | 31 |
Journal | ESAIM - Probability and Statistics |
Volume | 20 |
DOIs | |
Publication status | Published - 2016 |
Externally published | Yes |
Keywords
- Adaptive confidence bands
- Diffusion
- Drift estimation
- Ergodic Markov chain
- Functional central limit theorem
- Lepski's method
- Stationary density