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B0523
Title: Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift Authors:  Jakob Soehl - Delft University of Technology (Netherlands) [presenting]
Mathias Trabs - University of Hamburg (Germany)
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 us to construct confidence bands for the invariant density with optimal (up to undersmoothing) $L^{\infty}$-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.