Oracle P-values and variable screening
dc.contributor.author | Hao, Ning | |
dc.contributor.author | Zhang, Hao Helen | |
dc.date.accessioned | 2018-11-07T19:59:44Z | |
dc.date.available | 2018-11-07T19:59:44Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Hao, Ning; Zhang, Hao Helen. Oracle P-values and variable screening. Electron. J. Statist. 11 (2017), no. 2, 3251--3271. doi:10.1214/17-EJS1284. https://projecteuclid.org/euclid.ejs/1506931546 | en_US |
dc.identifier.issn | 1935-7524 | |
dc.identifier.doi | 10.1214/17-EJS1284 | |
dc.identifier.uri | http://hdl.handle.net/10150/630584 | |
dc.description.abstract | The concept of P-value was proposed by Fisher to measure inconsistency of data with a specified null hypothesis, and it plays a central role in statistical inference. For classical linear regression analysis, it is a standard procedure to calculate P-values for regression coefficients based on least squares estimator (LSE) to determine their significance. However, for high dimensional data when the number of predictors exceeds the sample size, ordinary least squares are no longer proper and there is not a valid definition for P-values based on LSE. It is also challenging to define sensible P-values for other high dimensional regression methods such as penalization and resampling methods. In this paper, we introduce a new concept called oracle P-value to generalize traditional P-values based on LSE to high dimensional sparse regression models. Then we propose several estimation procedures to approximate oracle P-values for real data analysis. We show that the oracle P-value framework is useful for developing new and powerful tools to enhance high dimensional data analysis, including variable ranking, variable selection, and screening procedures with false discovery rate (FDR) control. Numerical examples are then presented to demonstrate performance of the proposed methods. | en_US |
dc.description.sponsorship | National Science Foundations [DBI-1261830, DMS-1309507, DMS-1418172, NSFC-11571009] | en_US |
dc.language.iso | en | en_US |
dc.publisher | INST MATHEMATICAL STATISTICS | en_US |
dc.relation.url | https://projecteuclid.org/euclid.ejs/1506931546 | en_US |
dc.rights | Creative Commons Attribution 4.0 International License. Copyright is held by the author(s) or the publisher. If your intended use exceeds the permitted uses specified by the license, contact the publisher for more information. | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.subject | False discovery rate | en_US |
dc.subject | high dimensional data | en_US |
dc.subject | inference | en_US |
dc.subject | P-value | en_US |
dc.subject | variable selection | en_US |
dc.title | Oracle P-values and variable screening | en_US |
dc.type | Article | en_US |
dc.contributor.department | Univ Arizona, Dept Math | en_US |
dc.identifier.journal | ELECTRONIC JOURNAL OF STATISTICS | en_US |
dc.description.note | Open Access Journal. | en_US |
dc.description.collectioninformation | This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu. | en_US |
dc.eprint.version | Final published version | en_US |
dc.source.journaltitle | Electronic Journal of Statistics | |
dc.source.volume | 11 | |
dc.source.issue | 2 | |
dc.source.beginpage | 3251 | |
dc.source.endpage | 3271 | |
refterms.dateFOA | 2018-11-07T19:59:45Z |