A Smoothed Three-Part Redescending M-Estimator

Alistair J. Martin and Brenton R. Clarke ()
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Alistair J. Martin: School of Mathematics, Statistics, Chemistry and Physics, Murdoch University, Murdoch, WA 6150, Australia
Brenton R. Clarke: School of Mathematics, Statistics, Chemistry and Physics, Murdoch University, Murdoch, WA 6150, Australia

Stats, 2025, vol. 8, issue 2, 1-17

Abstract: 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.

Keywords: robust estimation; asymptotic variance; weak continuity; gross error sensitivity; change-of-variance sensitivity (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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