Some admissible nonparametric and related finite population sampling estimators (Q1067707)

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.