Theory of Probability and Mathematical Statistics
The trimmed mean in non-parametric regression function estimation
Subhra Sankar Dhar, Prashant Jha and Prabrisha Rakshit
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Abstract: This article studies a trimmed version of the Nadaraya–Watson estimator for the unknown non-parametric regression function. The characterization of the estimator through the minimization problem is established, and its pointwise asymptotic distribution is derived. The robustness property of the proposed estimator is also studied through the breakdown point. Moreover, similar to the trimmed mean in the location model, and for a wide range of trimming proportion, the proposed estimator possesses good efficiency and high breakdown point, which is out of the ordinary properties for any estimator. Furthermore, the usefulness of the proposed estimator is shown for two benchmark real data and various simulated data.
Keywords: Heavy-tailed distribution, Kernel density estimator, L-estimator, the Nadaraya–Watson estimator, Robust estimator
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