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October 2016 On high-dimensional misspecified mixed model analysis in genome-wide association study
Jiming Jiang, Cong Li, Debashis Paul, Can Yang, Hongyu Zhao
Ann. Statist. 44(5): 2127-2160 (October 2016). DOI: 10.1214/15-AOS1421

Abstract

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent genome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied by the limiting proportion of the nonzero random effects present in the LMM. The asymptotic results also establish convergence rate (in probability) of the REML estimators as well as a result regarding convergence of the asymptotic conditional variance of the REML estimator. The asymptotic results are fully supported by the results of empirical studies, which include extensive simulation studies that compare the performance of the REML estimator (under the misspecified LMM) with other existing methods, and real data applications (only one example is presented) that have important genetic implications.

Citation

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Jiming Jiang. Cong Li. Debashis Paul. Can Yang. Hongyu Zhao. "On high-dimensional misspecified mixed model analysis in genome-wide association study." Ann. Statist. 44 (5) 2127 - 2160, October 2016. https://doi.org/10.1214/15-AOS1421

Information

Received: 1 June 2014; Revised: 1 November 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1358.62095
MathSciNet: MR3546446
Digital Object Identifier: 10.1214/15-AOS1421

Subjects:
Primary: 62J99
Secondary: 60B20

Keywords: asymptotic property , heritability , misspecified LMM , MMMA , Random matrix theory , REML , variance components

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • October 2016
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