Bump detection in the presence of dependency: Does it ease or does it load?
Abstract
We provide the asymptotic minimax detection boundary for a bump, i.e. an abrupt change, in the mean function of a stationary Gaussian process. This will be characterized in terms of the asymptotic behavior of the bump length and height as well as the dependency structure of the process. A major finding is that the asymptotic minimax detection boundary is generically determined by the value of its spectral density at zero. Finally, our asymptotic analysis is complemented by non-asymptotic results for AR() processes and confirmed to serve as a good proxy for finite sample scenarios in a simulation study. Our proofs are based on laws of large numbers for non-independent and non-identically distributed arrays of random variables and the asymptotically sharp analysis of the precision matrix of the process.
Cite
@article{arxiv.1906.08017,
title = {Bump detection in the presence of dependency: Does it ease or does it load?},
author = {Farida Enikeeva and Axel Munk and Markus Pohlmann and Frank Werner},
journal= {arXiv preprint arXiv:1906.08017},
year = {2020}
}