Is consistent covariate selection compatible with adaptive estimation in semiparametric models? Florentina Bunea Florida State University Abstract: We suggest a model selection approach for estimation in semiparametric regression models. The compatibility of the following optimality aspects is studied: consistent covariate selection of the parametric component, asymptotic normality of the selected estimator of the parametric part and adaptive estimation of the nonparametric component. We show that these goals cannot be attained simultaneously by a direct extension of standard parametric or nonparametric model selection methods. and we introduce a new type of penalization, tailored to semiparametric models. The form of the penalty term depends on whether one uses a one stage or a two stage estimation procedures. We illustrate our method for two important models: partially linear regression and semiparametric hazard function regression models, and also address some computational issues.