Minimax optimality of CUSUM for an autoregressive model

Knoth, Sven; Frisén, Marianne

doi:10.1111/j.1467-9574.2012.00512.x

Minimax optimality of CUSUM for an autoregressive model

Publication date

2012-05-07

Document type

Forschungsartikel

Author

Knoth, Sven

Frisén, Marianne

Organisational unit

Rechnergestützte Statistik

DOI

10.1111/j.1467-9574.2012.00512.x

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/21907

Scopus ID

2-s2.0-84867398662

Publisher

Wiley

Series or journal

Statistica Neerlandica

ISSN

1467-9574

Periodical volume

66

Periodical issue

4

First page

357

Last page

379

Part of the university bibliography

✅

Language

English

Keyword

Autoregressive

Change point

Monitoring

Online detection

Abstract

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others, the change is in the unconditional distribution. Some models include an observation before the first possible change time – others not. Earlier and new CUSUM type methods are given, and minimax optimality is examined. For the conditional model with an observation before the possible change, there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations, it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.

Version

Published version

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