THE TRIMMED MEAN IN NON-PARAMETRIC REGRESSION FUNCTION ESTIMATION

被引：1

作者：

Dhar, Subhra Sankar ^{[1
]}

Jha, Prashant ^{[2
]}

Rakshit, Prabrisha ^{[3
]}

机构：

[1] IIT Kanpur, Dept Math & Stat, Kanpur, India

[2] NIT Sikkim, Dept Math, Sikkim, India

[3] Rutgers State Univ, Dept Stat, New Brunswick, NJ USA

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2022年

关键词：

Heavy-tailed distribution; Kernel density estimator; L-estimator; the Nadaraya-Watson estimator; Robust estimator; ASYMPTOTIC-DISTRIBUTION; ROBUST ESTIMATORS; PREDICTION;

D O I：

10.1090/tpms/1174

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：133 / 158

页数：26

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