Due to the hardness of order statistics, finite sample bias of robust statistics is generally unsolvable. Monte Carlo method can provide approximate solutions, but the convergence rate is very low, so the computational cost to achieve desired accuracy is unaffordable for ordinary users. Here, with a comparametric approach, the distribution structure of order statistics is decomposed. By obtaining a set of quasi-random variables simultaneously consistent for two or more different estimators, the finite sample bias of other related estimators can be approximated with much less computational costs. This article provides a different and prospective approach to integrate two or more parametric assumptions.
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, e.g., https://github.com/tubanlee/FiniteSampleBias). I am introducing this work in YouTube, Quora, and stackexchange, if you are interested, please visit: https://www.youtube.com/@Iobiomathematics or https://www.quora.com/profile/Tuobang-Li-1/answers or https://stats.stackexchange.com/users/406413/tuobang-li . Also, the manuscript has been deposited in Zenodo. Tuobang Li. (2024). Robust estimations from distribution structures: V. Non-asymptotic. https://doi.org/10.5281/zenodo.10616689 or https://www.researchgate.net/publication/377974622_Robust_estimations_from_distribution_structures_V_Non-Asymptotic
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