Asymptotic Properties Of LS-SCAD Estimators In Generalized Linear Models

Generalized linear models(GLMs),which can model a large variety of data,have a wide area of application.The class of GLMs includes,as special cases,linear regression,analysis-of-variance models,log-linear models for the analysis of contingency tables,logistic models for binary data in the form of proportions and many others.Variable selection is fundamental to high-dimensional statistical modeling.But classical subset variable selection method is not computationally feasible when its dimensional is large,and the method of subset selection is a discrete and non-continuous process,so the estimator is not stable enough.In the literature, several variable selection methods have been studied extensively.In this paper,we study the asymptotic properties of the SCAD-penalized least squares estimator in sparse,high dimensional,generalized linear model.The SCAD-penalized least squares estimators performs well in computation and stability.Under mild conditions,we prove that the SCAD-penalized least squares estimators are consistent and asymptotically normal when the number of covariates may increase to infinity with the sample size.We are particularly interested in the use of this estimator for variable selecting and estimating simultaneously.We show that under appropriate conditions,the SCAD-penalized least squares estimator is consistent for variable selection and that the estimators of nonzero coefficients have the same asymptotic distribution as they would have if the zero coefficients were known in advance.Simulation studies indicate that this estimator performs well in terms of variable selection and estimation.