Abstract

For partial linear model Y = X

τ

β
0 + g
0(T) + ε with unknown β
0 ∈¸ R

d
and an unknown smooth function g
0, this paper considers the Huber-Dutter estimators of β
0, scale σ for the errors and the function g
0 respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β
0 and σ are asymptotically normal with convergence rate n
-1/2 and the B-spline Huber-Dutter estimator of g
0 achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β
0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.