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