  Although genome-wide association studies (GWAS) on complex traits have
achieved great successes, the current leading GWAS approaches simply perform to
test each genotype-phenotype association separately for each genetic variant.
Curiously, the statistical properties for using these approaches is not known
when a joint model for the whole genetic variants is considered. Here we
advance in GWAS in understanding the statistical properties of the "population
structure correction" (PSC) approach, a standard univariate approach in GWAS.
We further propose and analyse a correction to the PSC approach, termed as
"corrected population correction" (CPC). Together with the theoretical results,
numerical simulations show that CPC is always comparable or better than PSC,
with a dramatic improvement in some special cases.
