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    Oracle P-values and variable screening

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    Author
    Hao, Ning
    Zhang, Hao Helen
    Affiliation
    Univ Arizona, Dept Math
    Issue Date
    2017
    Keywords
    False discovery rate
    high dimensional data
    inference
    P-value
    variable selection
    
    Metadata
    Show full item record
    Publisher
    INST MATHEMATICAL STATISTICS
    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
    Journal
    ELECTRONIC JOURNAL OF STATISTICS
    Rights
    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
    1935-7524
    DOI
    10.1214/17-EJS1284
    Version
    Final published version
    Sponsors
    National Science Foundations [DBI-1261830, DMS-1309507, DMS-1418172, NSFC-11571009]
    Additional Links
    https://projecteuclid.org/euclid.ejs/1506931546
    ae974a485f413a2113503eed53cd6c53
    10.1214/17-EJS1284
    Scopus Count
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    UA Faculty Publications

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