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We study behavior of the restricted maximum likelihood (REML) estimator undera misspecified linear mixed model (LMM) that has received much attention inrecent gnome-wide association studies. The asymptotic analysis establishesconsistency of the REML estimator of the variance of the errors in the LMM, andconvergence in probability of the REML estimator of the variance of the randomeffects in the LMM to a certain limit, which is equal to the true variance ofthe random effects multiplied by the limiting proportion of the nonzero randomeffects present in the LMM. The aymptotic results also establish convergencerate (in probability) of the REML estimators as well as a result regardingconvergence of the asymptotic conditional variance of the REML estimator. Theasymptotic results are fully supported by the results of empirical studies,which include extensive simulation studies that compare the performance of theREML estimator (under the misspecified LMM) with other existing methods.

High-dimensional genome-wide association study and misspecified mixed model analysis