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

View

Related Concepts

Estimator Mathematics Invariant measure Ergodic theory Markov chain Invariant (physics) Central limit theorem Measure (data warehouse) Applied mathematics Ergodicity Mathematical analysis Statistics Computer science Mathematical physics Database

Jakob Söhl , Mathias Trabs ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1051/ps/2016017 · OA: W1578369061

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