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Some admissible nonparametric and related finite population sampling estimators. (English) Zbl 0581.62006
Let \(X_ 1,...,X_ n\) be i.i.d. r.v.’s with an unknown d.f. \(F\in \{F:\int | \Phi (t)| dF(t)<\infty \}\) (\(\Phi\) is some specific function) and let \(\delta\) be an estimator of \(\gamma (F)=\int \Phi (t)dF(t)\) with squared error loss function.
In the article a condition for \(\delta\) to be an admissible estimator of \(\gamma\) (F) is given. The duality between admissible estimators in the finite population problem and the admissible ones in the nonparametric problem is demonstrated.
Reviewer: R.Mnatsakanov

62C15 Admissibility in statistical decision theory
62G05 Nonparametric estimation
62D05 Sampling theory, sample surveys
62C10 Bayesian problems; characterization of Bayes procedures
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