Title: Variable Selection for Highly Correlated Predictors,
Abstract: Penalty-based variable selection methods are powerful in selecting relevant
covariates and estimating coefficients simultaneously. However, variable
selection could fail to be consistent when covariates are highly correlated.
The partial correlation approach has been adopted to solve the problem with
correlated covariates. Nevertheless, the restrictive range of partial
correlation is not effective for capturing signal strength for relevant
covariates. In this paper, we propose a new Semi-standard PArtial Covariance
(SPAC) which is able to reduce correlation effects from other predictors while
incorporating the magnitude of coefficients. The proposed SPAC variable
selection facilitates choosing covariates which have direct association with
the response variable, via utilizing dependency among covariates. We show that
the proposed method with the Lasso penalty (SPAC-Lasso) enjoys strong sign
consistency in both finite-dimensional and high-dimensional settings under
regularity conditions. Simulation studies and the `HapMap' gene data
application show that the proposed method outperforms the traditional Lasso,
adaptive Lasso, SCAD, and Peter-Clark-simple (PC-simple) methods for highly
correlated predictors.