Genetic association study is an essential step to discover genetic factors
that are associated with a complex trait of interest. In this paper we present
a novel generalized quasi-likelihood score (GQLS) test that is suitable for a
study with either a quantitative trait or a binary trait. We use a logistic
regression model to link the phenotypic value of the trait to the distribution
of allelic frequencies. In our model, the allele frequencies are treated as a
response and the trait is treated as a covariate that allows us to leave the
distribution of the trait values unspecified.
In a Gaussian graphical model, the conditional independence between two
variables are characterized by the corresponding zero entries in the inverse
covariance matrix. Maximum likelihood method using the smoothly clipped
absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO
penalty (Zou, 2006) have been proposed in literature. In this article, we
establish the result that using Bayesian information criterion (BIC) to select
the tuning parameter in penalized likelihood estimation with both types of
penalties can lead to consistent graphical model selection.