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euclid.ejs.1506931546.pdf
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INST MATHEMATICAL STATISTICSCitation
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/1506931546Journal
ELECTRONIC JOURNAL OF STATISTICSRights
Creative Commons Attribution 4.0 International License.Collection Information
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.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.Note
Open Access Journal.ISSN
1935-7524Version
Final published versionSponsors
National Science Foundations [DBI-1261830, DMS-1309507, DMS-1418172, NSFC-11571009]Additional Links
https://projecteuclid.org/euclid.ejs/1506931546ae974a485f413a2113503eed53cd6c53
10.1214/17-EJS1284