An adaptive test on high-dimensional parameters in generalized linear models

Chong Wu, Gongjun Xu, Wei Pan

Research output: Contribution to journalArticlepeer-review

Abstract

Significance testing for high-dimensional generalized linear models (GLMs) has become increasingly important in various applications. However, existing methods are mainly based on a sum of the squares of the elements of the score vector and are only powerful under certain alternative hypotheses. In practice, the density of the true association pattern under an alternative hypothesis dictates whether existing tests are powerful. We propose an adaptive test on a high-dimensional parameter of a GLM (in the presence of a low-dimensional nuisance parameter) that maintains high power across a wide range of scenarios. To evaluate its p-value, its asymptotic null distribution is derived. We conduct simulations to demonstrate the superior performance of the proposed test. In addition, we apply it and other existing tests to an Alzheimer's Disease Neuroimaging Initiative data set to detect possible associations between Alzheimer's disease and gene pathways that have a large number of single nucleotide polymorphisms (SNPs). We implemented the proposed method in the R package GLMaSPU, which is publicly available on GitHub and CRAN.

Original languageEnglish (US)
Pages (from-to)2163-2186
Number of pages24
JournalStatistica Sinica
Volume29
Issue number4
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
The authors thank the reviewers and editors for their helpful comments. This research was supported by NIH grants R01GM113250, R01HL105397, and R01HL116720, by NSF grants DMS-1712717 and SES-1659328, by NSA grant H98230-17-1-0308, and by the Minnesota Supercomputing Institute. CW was supported by a University of Minnesota Doctoral Dissertation Fellowship. The data collection and sharing for this project were funded by the Alzheimer’s Dis- ease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904).

Funding Information:
The authors thank the reviewers and editors for their helpful comments. This research was supported by NIH grants R01GM113250, R01HL105397, and R01HL116720, by NSF grants DMS-1712717 and SES-1659328, by NSA grant H98230-17-1-0308, and by the Minnesota Supercomputing Institute. CW was supported by a University of Minnesota Doctoral Dissertation Fellowship. The data collection and sharing for this project were funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904).

Publisher Copyright:
© 2020 Institute of Statistical Science. All rights reserved.

Keywords

  • Adaptive tests
  • Generalized linear models
  • High-dimensional testing
  • Power

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