Theoretical derivation determines the exact variance of third moment unbiased estimators and approximates fourth moment variance, highlighting precision bounds for static statistical models.
This article is the sequel to https://doi.org/10.1002/qre.70038 where the author developed the third and fourth moment unbiased estimators from any underlying distribution under the simplest static statistical model, x i = μ + ε i , for sample sizes n ≥ 4. The objective now is to obtain the exact variance of the third moment unbiased estimator and to approximate that of the fourth moment.
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Maghsoodloo et al. (2026) studied this question.
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