In this paper we propose the Gini correlation screening(GCS)method to select the important variables with ultrahigh dimensional data.The new procedure is based on the Gini correlation coefficient via the covariance between the response and the rank of the predictor variables rather than the Pearson correlation and the Kendallτcorrelation coefficient.The new method does not require imposing a specific model structure on regression functions and only needs the condition which the predictors and response have continuous distribution function.We demonstrate that,with the number of predictors growing at an exponential rate of the sample size,the proposed procedure possesses consistency in ranking,which is both useful in its own right and can lead to consistency in selection.The procedure is computationally efficient and simple,and exhibits a competent empirical performance in our intensive simulations and real data analysis.
In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.
