Consistent covariate selection and post model selection inference in semiparametric regression

Details Consistent covariate selection and post model selection inference in semiparametric regression Consistent covariate selection and post model selection inference in semiparametric regression

2004-06-23

arxiv.org/abs/math/0406465v1

Annals of Statistics 2004, Vol. 32, No. 3, 898-927

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000247

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.

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