Bump detection in the presence of dependency: Does it ease or does it load?
| Autor: | Farida Enikeeva, Axel Munk, Frank Werner, Markus Pohlmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Asymptotic analysis Boundary (topology) Mathematics - Statistics Theory Statistics Theory (math.ST) ARMA processes 01 natural sciences 010104 statistics & probability symbols.namesake change point detection Law of large numbers weak laws of large numbers minimax testing FOS: Mathematics 0101 mathematics Gaussian process Mathematics 010102 general mathematics Mathematical analysis Function (mathematics) Minimax Toeplitz matrices symbols time series Random variable Change detection |
| Zdroj: | Bernoulli 26, no. 4 (2020), 3280-3310 |
| Popis: | 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($p$) 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. |
| Databáze: | OpenAIRE |
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