In partially linear single-index models, we obtain the profile least-squares estimators of regression coefficients, which are semiparametrically efficient. 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, is able to identify the true model consistently. Finally, we develop two test statistics to identify parametric components and check nonparametric function, respectively.