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TITLE: Variable Selection in Linear Mixed Effects Models
SPEAKER: Professor Yingying Fan
ABSTRACT:
This
paper is concerned with the selection and estimation of fixed and
random effects in linear mixed effects models. We propose a class of
nonconcave penalized profile likelihood methods for selecting and
estimating significant fixed effects parameters simultaneously for the
setting in which the number of predictors is allowed to grow
exponentially with sample size.
To study the sampling properties of the proposed procedure, we establish
a new theoretical framework which is distinguished from the existing
ones (Fan and Li, 2001). We show that the proposed procedure enjoys the
model selection consistency. We further propose a group variable
selection strategy to simultaneously select and estimate the significant
random effects. The resulting random effects estimator is compared with
the oracle-assisted Bayes estimator. We prove that, with probability
tending to one, the proposed procedure identifies all true random
effects, and furthermore, that the resulting estimates are close to the
oracle-assisted Bayes estimates for the selected random effects. In the
random effects selection and estimation, the dimensionality is also
allowed to increase exponentially with sample size. Monte Carlo
simulation studies are conducted to examine the finite sample
performances of the proposed procedures. We further illustrate the
proposed procedures via a real data example.
