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 medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.
The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al.(2008) proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized likelihood ratio test is established. Under the null hypotheses the normalized test statistic follows a χ2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance parameters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.
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.
