On high-dimensional misspecified mixed model analysis in genome-wide association study

Jiming Jiang, Cong Li, Debashis Paul, Can YANG, Hongyu Zhao

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)
1 Downloads (Pure)

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 misspeci fied LMM) with other existing methods, and real data applications (only one example is presented) that have important genetic implications.

Original languageEnglish
Pages (from-to)2127-2160
Number of pages34
JournalAnnals of Statistics
Volume44
Issue number5
DOIs
Publication statusPublished - Oct 2016

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic property
  • Heritability
  • Misspecified LMM
  • MMMA
  • Random matrix theory
  • REML
  • Variance components

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