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 si-multanously 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.
These works have been publically deposited in this Github since one year ago for a PNAS paper (I hidden some previous versions after updated new versions, https://github.com/tubanlee/NRS3333). I am introducing this work in YouTube and Quora, if you are interested, please visit: https://www.youtube.com/@Iobiomathematics or https://www.quora.com/profile/Tuobang-Li-1/answers . Also, the manuscript has been deposited in Zenodo Tuobang Li. (2022). Robust estimations for semiparametric models: Moments. https://doi.org/10.5281/zenodo.8127703 and research gate https://www.researchgate.net/publication/377974419_Robust_estimations_from_distribution_structures_III_Invariant_Moments .
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