Article
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Robust Estimations from Distribution Structures: III. Invariant Moments
Version 1
: Received: 13 February 2024 / Approved: 14 February 2024 / Online: 14 February 2024 (14:07:20 CET)
How to cite: Li, T. Robust Estimations from Distribution Structures: III. Invariant Moments. Preprints 2024, 2024020817. https://doi.org/10.20944/preprints202402.0817.v1 Li, T. Robust Estimations from Distribution Structures: III. Invariant Moments. Preprints 2024, 2024020817. https://doi.org/10.20944/preprints202402.0817.v1
Abstract
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a class of estimators, consistent simultanously for both a semiparametric distribution and a distinct parametric distribution, is proposed. These efficient estimators are robust to both gross errors and departures from parametric assumptions, making them ideal for estimating the mean and central moments of common unimodal distributions. This article also illuminates the understanding of the common nature of probability distributions and the measures of them.
Keywords
moments; invariant; unimodal; adaptive estimation; U-statistics
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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