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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jan 1, 2005
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