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Robust estimations from distribution structures: III. Invariant Moment

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  • Li, Tuobang

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.

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  • Li, Tuobang, 2024. "Robust estimations from distribution structures: III. Invariant Moment," OSF Preprints 5jmz9, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:5jmz9
    DOI: 10.31219/osf.io/5jmz9
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