Weak Convergence of the Regularization Path in Penalized M-Estimation
AbstractWe consider a function defined as the pointwise minimization of a doubly index random process. We are interested in the weak convergence of the minimizer in the space of bounded functions. Such convergence results can be applied in the context of penalized M-estimation, that is, when the random process to minimize is expressed as a goodness-of-fit term plus a penalty term multiplied by a penalty weight. This weight is called the "regularization parameter" and the minimizing function the "regularization path". The regularization path can be seen as a collection of estimators indexed by the regularization parameter. We obtain a consistency result and a central limit theorem for the regularization path in a functional sense. Various examples are provided, including the ℓ-super-1-regularization path for general linear models, the ℓ-super-1- or ℓ-super-2-regularization path of the least absolute deviation regression and the Akaike information criterion. Copyright (c) 2010 Board of the Foundation of the Scandinavian Journal of Statistics.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.
Volume (Year): 37 (2010)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Ban Zheng & Eric Moulines & Fr\'ed\'eric Abergel, 2012. "Price Jump Prediction in Limit Order Book," Papers 1204.1381, arXiv.org.
- Ban Zheng & Eric Moulines & Frédéric Abergel, 2013. "Price jump prediction in a limit order book," Post-Print hal-00684716, HAL.
- repec:hal:wpaper:hal-00684716 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
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.