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2017 Oracle P-values and variable screening
Ning Hao, Hao Helen Zhang
Electron. J. Statist. 11(2): 3251-3271 (2017). DOI: 10.1214/17-EJS1284

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.

Citation

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Ning Hao. Hao Helen Zhang. "Oracle P-values and variable screening." Electron. J. Statist. 11 (2) 3251 - 3271, 2017. https://doi.org/10.1214/17-EJS1284

Information

Received: 1 December 2014; Published: 2017
First available in Project Euclid: 2 October 2017

zbMATH: 06790060
MathSciNet: MR3708538
Digital Object Identifier: 10.1214/17-EJS1284

JOURNAL ARTICLE
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Vol.11 • No. 2 • 2017
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