Valid Confidence Intervals In Regression After Variable Selection
AbstractWe consider a linear regression model with regression parameters ( 1,..., p) and error variance parameter 2. Our aim is to find a confidence interval with minimum coverage probability 1 for a parameter of interest 1 in the presence of nuisance parameters ( 2,..., p, 2). We consider two confidence intervals, the first of which is the standard confidence interval for 1 with coverage probability 1 . The second confidence interval for 1 is obtained after a variable selection procedure has been applied to p. This interval is chosen to be as short as possible subject to the constraint that it has minimum coverage probability 1 . The confidence intervals are compared using a risk function that is defined as a scaled version of the expected length of the confidence interval. We show that, subject to certain conditions including that (dimension of response vector) p is small, the second confidence interval is preferable to the first when we anticipate (without being certain) that p / is small. This comparison of confidence intervals is shown to be mathematically equivalent to a corresponding comparison of prediction intervals.
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.
Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 14 (1998)
Issue (Month): 04 (August)
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:email@example.com
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Farchione, David & Kabaila, Paul, 2008. "Confidence intervals for the normal mean utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1094-1100, July.
- Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation for Research in Economics, Yale University.
- Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.
- Kabaila, Paul & Giri, Khageswor, 2009. "Large-sample confidence intervals for the treatment difference in a two-period crossover trial, utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 652-658, March.
- Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
- Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters).
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.