Minimax Optimality of CUSUM for an Autoregressive Model
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.
|Date of creation:||10 Feb 2011|
|Date of revision:|
|Publication status:||Forthcoming as Knoth, Sven and Marianne Frisén, 'Minimax Optimality of CUSUM for an Autoregressive Model' in Statistica Neerlandica.|
|Contact details of provider:|| Postal: Statistical Research Unit, University of Gothenburg, Box 640, SE 40530 GÖTEBORG|
Web page: http://www.statistics.gu.se/
When requesting a correction, please mention this item's handle: RePEc:hhs:gunsru:2011_004. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Linus Schiöler)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.