Mathematics – Statistics Theory
Scientific paper
2009-03-31
Annals of Statistics 2009, Vol. 37, No. 2, 673-696
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/07-AOS580 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/07-AOS580
We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneously for the linear and nonparametric components. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property, in the sense that it is asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. The finite sample behavior of the SCAD-penalized estimators is evaluated with simulation and illustrated with a data set.
Huang Jian
Xie Huiliang
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