Convergence rates for estimation in certain partially linear models

Abstract Rates of convergence are studied for estimation in certain partial linear models that include nonparametric regression models with discontinuous derivatives. The asymptotic behavior of two smoothing spline related estimators of the regression coefficient and regression function in these models are examined. Lower bounds are then derived for rates of convergence in estimating the size of jump discontinuities in a regression function or its derivative. The latter rates are nonparametric which indicates that parametric convergence rates are not possible in such instances.