A smoothed three-part redescending M-estimator

Alistair J. Martin; Brenton R. Clarke

doi:10.3390/stats8020033

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A smoothed three-part redescending M-estimator

Journal article

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Peer reviewed

A smoothed three-part redescending M-estimator

Alistair J. Martin and Brenton R. Clarke

Stats, Vol.8(2), 33

2025

DOI: https://doi.org/10.3390/stats8020033

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Abstract

robust estimation

asymptotic variance

weak continuity

gross error sensitivity

change-of-variance sensitivity

Statistics

Expanding knowledge in the mathematical sciences

A smoothed M-estimator is derived from Hampel’s three-part redescending estimator for location and scale. The estimator is shown to be weakly continuous and Fréchet differentiable in the neighbourhood of the normal distribution. Asymptotic assessment is conducted at asymmetric contaminating distributions, where smoothing is shown to improve variance and change-of-variance sensitivity. Other robust metrics compared are largely unchanged, and therefore, the smoothed functions represent an improvement for asymmetric contamination near the rejection point with little downside.

Details

Title: A smoothed three-part redescending M-estimator
Authors/Creators: Alistair J. Martin (Author) - Murdoch University, School of Mathematics, Statistics, Chemistry and Physics
Brenton R. Clarke (Corresponding Author) - Murdoch University, School of Mathematics, Statistics, Chemistry and Physics
Publication Details: Stats, Vol.8(2), 33
Publisher: MDPI; BASEL
Number of pages: 17
Identifiers: 991005765532107891
Murdoch Affiliation: School of Mathematics, Statistics, Chemistry and Physics
Language: English
Resource Type: Journal article

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