Seminar Announcements

In this talk, I will discuss how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models

 consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion.

Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear

models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate

model selection for the nonparametric components for each submodel. This leads to very heavy computational burden. We propose a

class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood.  We establish the

rate of convergence of the resulting estimate.  With proper choices of penalty functions and regularization parameters, we show the

asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle

procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component.

 We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chi-squared

distribution, which is independent of the nuisance parameters.  Extensive Monte Carlo simulation studies are conducted to examine the finite

sample performance of the proposed variable selection procedures.