We consider the problem of simultaneous variable selection and estimation inpartially linear models with a divergent number of covariates in the linearpart, under the assumption that the vector of regression coefficients issparse. We apply the SCAD penalty to achieve sparsity in the linear part anduse polynomial splines to estimate the nonparametric component. Underreasonable conditions, it is shown that consistency in terms of variableselection and estimation can be achieved simultaneously for the linear andnonparametric components. Furthermore, the SCAD-penalized estimators of thenonzero coefficients are shown to have the asymptotic oracle property, in thesense that it is asymptotically normal with the same means and covariances thatthey would have if the zero coefficients were known in advance. The finitesample behavior of the SCAD-penalized estimators is evaluated with simulationand illustrated with a data set.
展开▼
