Open Access
December 2017 A likelihood ratio framework for high-dimensional semiparametric regression
Yang Ning, Tianqi Zhao, Han Liu
Ann. Statist. 45(6): 2299-2327 (December 2017). DOI: 10.1214/16-AOS1483


We propose a new inferential framework for high-dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high-dimensional data analysis, including incomplete data, selection bias and heterogeneity. Our work has three main contributions: (i) We develop a regularized statistical chromatography approach to infer the parameter of interest under the proposed semiparametric generalized linear model without the need of estimating the unknown base measure function. (ii) We propose a new likelihood ratio based framework to construct post-regularization confidence regions and tests for the low dimensional components of high-dimensional parameters. Unlike existing post-regularization inferential methods, our approach is based on a novel directional likelihood. (iii) We develop new concentration inequalities and normal approximation results for U-statistics with unbounded kernels, which are of independent interest. We further extend the theoretical results to the problems of missing data and multiple datasets inference. Extensive simulation studies and real data analysis are provided to illustrate the proposed approach.


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Yang Ning. Tianqi Zhao. Han Liu. "A likelihood ratio framework for high-dimensional semiparametric regression." Ann. Statist. 45 (6) 2299 - 2327, December 2017.


Received: 1 December 2015; Revised: 1 May 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838134
MathSciNet: MR3737893
Digital Object Identifier: 10.1214/16-AOS1483

Primary: 62E20 , 62G20
Secondary: 62G10

Keywords: Confidence interval , likelihood ratio test , nonconvex penalty , Post-regularization inference , semiparametric sparsity , U-statistics

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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