Consistency of spike and slab regression
Spike and slab models are a popular and attractive variable selection approach in regression settings. Applications for these models have blossomed over the last decade and they are increasingly being used in challenging problems. At the same time, theory for spike and slab models has not kept pace with the applications. There are many gaps in what we know about their theoretical properties. An important property known to hold in these models is selective shrinkage: a unique property whereby the posterior mean is shrunk toward zero for non-informative variables only. This property has been shown to hold under orthogonality for continuous priors under the modified class of rescaled spike and slab models. In this paper, we extend this result to the general case and prove an oracle property for the posterior mean under a discrete two-component prior. An immediate consequence is that a strong selective shrinkage property holds. Interestingly, the conditions needed for our result to hold in the non-orthogonal setting are more stringent than in the orthogonal case and amount to a type of enforced sparsity condition that must be met by the prior.
If 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.
Volume (Year): 81 (2011)
Issue (Month): 12 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
- Geweke, John & Meese, Richard, 1981.
"Estimating regression models of finite but unknown order,"
Journal of Econometrics,
Elsevier, vol. 16(1), pages 162-162, May.
- Geweke, John F & Meese, Richard, 1981. "Estimating Regression Models of Finite but Unknown Order," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 55-70, February.
- Ishwaran H. & Rao J.S., 2003. "Detecting Differentially Expressed Genes in Microarrays Using Bayesian Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 438-455, January.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
- Ishwaran, Hemant & Rao, J. Sunil, 2005. "Spike and Slab Gene Selection for Multigroup Microarray Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 764-780, September. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1920-1928. 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: (Dana Niculescu)
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.