  In partially linear single-index models, we obtain the semiparametrically
efficient profile least-squares estimators of regression coefficients. We also
employ the smoothly clipped absolute deviation penalty (SCAD) approach to
simultaneously select variables and estimate regression coefficients. We show
that the resulting SCAD estimators are consistent and possess the oracle
property. Subsequently, we demonstrate that a proposed tuning parameter
selector, BIC, identifies the true model consistently. Finally, we develop a
linear hypothesis test for the parametric coefficients and a goodness-of-fit
test for the nonparametric component, respectively. Monte Carlo studies are
also presented.
