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Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

Acta Mathematicae Applicatae Sinica , Volume 21 (2) – Jan 1, 2005

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.

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-005-0234-y
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2005

References