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Abstract: In this paper, we are concerned with how to select significant variables insemiparametric modeling. Variable selection for semiparametric regressionmodels consists of two components: model selection for nonparametric componentsand selection of significant variables for the parametric portion. Thus,semiparametric variable selection is much more challenging than parametricvariable selection e.g., linear and generalized linear models becausetraditional variable selection procedures including stepwise regression and thebest subset selection now require separate model selection for thenonparametric components for each submodel. This leads to a very heavycomputational burden. In this paper, we propose a class of variable selectionprocedures for semiparametric regression models using nonconcave penalizedlikelihood. We establish the rate of convergence of the resulting estimate.With proper choices of penalty functions and regularization parameters, we showthe asymptotic normality of the resulting estimate and further demonstrate thatthe proposed procedures perform as well as an oracle procedure. Asemiparametric generalized likelihood ratio test is proposed to selectsignificant variables in the nonparametric component. We investigate theasymptotic behavior of the proposed test and demonstrate that its limiting nulldistribution follows a chi-square distribution which is independent of thenuisance parameters. Extensive Monte Carlo simulation studies are conducted toexamine the finite sample performance of the proposed variable selectionprocedures.

Author: Runze Li, Hua Liang


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