Abstract
This paper studies robust estimation of multivariate regression model using kernel weighted local linear regression. A robust estimation procedure is proposed for estimating the regression function and its partial derivatives. The proposed estimators are jointly asymptotically normal and attain nonparametric optimal convergence rate. One-step approximations to the robust estimators are introduced to reduce computational burden. The one-step local M-estimators are shown to achieve the same efficiency as the fully iterative local M-estimators as long as the initial estimators are good enough. The proposed estimators inherit the excellent edge-effect behavior of the local polynomial methods in the univariate case and at the same time overcome the disadvantages of the local least-squares based smoothers. Simulations are conducted to demonstrate the performance of the proposed estimators. Real data sets are analyzed to illustrate the practical utility of the proposed methodology.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10471006).
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Li, J., Zheng, M. Robust estimation of multivariate regression model. Stat Papers 50, 81–100 (2009). https://doi.org/10.1007/s00362-007-0063-6
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DOI: https://doi.org/10.1007/s00362-007-0063-6