Consistency and normality of Huber-Dutter estimators for partial linear model

For partial linear model Y = X-tau beta(0) + g(0)(T) + epsilon with unknown beta(0)is an element of R-d and an unknown smooth function g(0), this paper considers the Huber-Dutter estimators of beta(0), scale sigma for the errors and the function g(0) approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of beta(0) and sigma are shown to be asymptotically normal with the rate of convergence n(-1/2) and the B-spline Huber-Dutter estimator of g(0) achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of beta(0) is competitive with its M-estimator without scale parameter and the ordinary least square estimator.