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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

##### MSC:
 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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