| Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially linear model to estimate the nonparametric component, when both the number of knots and the penalty factor vary with the sample size. We obtain mean-square convergence rates and establish asymptotic distributional approximations, with valid standard errors, for the resulting multivariate estimators of both the parametric and nonparametric components in this model. Our results extend and complement the recent theoretical work in the literature on penalized spline estimators by allowing for multivariate covariates, heteroskedasticity of unknown form, derivative estimation, and statistical inference in the semi-linear model, using weaker assumptions. The results from a simulation study are also reported. |
