Statistics and Its Interface

Volume 14 (2021)

Number 2

Penalized empirical likelihood for high-dimensional generalized linear models

Pages: 83 – 94

DOI: https://dx.doi.org/10.4310/20-SII615

Authors

Xia Chen (School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, China)

Liyue Mao (School of Finance and Economics Management, Chongqing College of Electronic Engineering, Chongqing, China)

Abstract

We develop penalized empirical likelihood for parameter estimation and variable selection in high-dimensional generalized linear models. By using adaptive lasso penalty function, we show that the proposed estimator has the oracle property. Also, we consider the problem of testing hypothesis, and show that the nonparametric profiled empirical likelihood ratio statistic has asymptotic chi-square distribution. Some simulations and an application are given to illustrate the performance of the proposed method.

Keywords

penalized empirical likelihood, high-dimensional data, variable selection, generalized linear model

2010 Mathematics Subject Classification

62F12, 62J12

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This research is supported by the Youth Fund for Humanities and Social Sciences Research of Ministry of Education (No. 18YJC910003), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2020JM-276) and the Fundamental Research Funds for the Central Universities (No. GK201901008).

Received 9 August 2019

Accepted 5 April 2020

Published 22 December 2020