Consistency and normality of Huber-Dutter estimators for partial linear model |
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Authors: | XingWei Tong HengJian Cui Peng Yu |
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Affiliation: | (1) School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China;(2) National Geomatics Center of China, Beijing, 100873, China |
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Abstract: | For partial linear model Y = X τ β 0 + g 0(T) + ∈ with unknown β 0 ∈ ȑ 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 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β 0 and σ 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 β 0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10671106, 10771017) |
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Keywords: | Huber-Dutter estimator partial linear model B-spline function |
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