REML estimators in High-Dimensional Kernel Linear Mixed Models

Music City Center 

REstricted Maximum Likelihood (REML) estimators are commonly used to produce unbiased estimators for the variance components in linear mixed models. Nowadays, the dimension of the design matrix with respect to the random effects may be high, especially in genetic association studies. Originating from this, I will first introduce the high-dimensional kernel linear mixed models. The REML equations will be derived followed by a discussion on the consistency of REML estimators for some commonly used kernel matrices. The validity of the theories is demonstrated via some simulation studies.

Kernel Methods

Inner Product Random Matrices

Restricted Maximum Likelihood Estimator

Consistency 

Section on Statistical Learning and Data Science