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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



The trimmed mean in non-parametric regression function estimation

Authors: Subhra Sankar Dhar, Prashant Jha and Prabrisha Rakshit
Journal: Theor. Probability and Math. Statist. 107 (2022), 133-158
MSC (2020): Primary 62G08; Secondary 62G05
Published electronically: November 8, 2022
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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.

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Additional Information

Subhra Sankar Dhar
Affiliation: Department of Mathematics and Statistics, IIT Kanpur, Kanpur, India

Prashant Jha
Affiliation: Department of Mathematics, NIT Sikkim, Sikkim, India

Prabrisha Rakshit
Affiliation: Department of Statistics, Rutgers University, USA

Keywords: Heavy-tailed distribution, Kernel density estimator, $L$-estimator, the Nadaraya–Watson estimator, Robust estimator
Received by editor(s): March 31, 2021
Accepted for publication: October 23, 2021
Published electronically: November 8, 2022
Additional Notes: The first author is partially supported by MATRICS (MTR/2019/000039), a research grant from the SERB, Government of India.
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv