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The problem to be analyzed in this paper deals with the finding of n values x1, x2, ..., xn ∈ R which minimize the function:E [míni=1,...,n c (ξ - xi)]where ξ is a one-dimensional random variable with known distribution function φ and c is a measurable and positive function.First, conditions on c in order to ensure the existence of a solution to this problem are determined. Next, necessary conditions to be satisfied by the point (x1, x2, ..., xn) in which the function attains the minimum are looked...
The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.
R-ε criterion is considered in a decision problem (Θ, D*, R). Some considerations are made for the case in which the parameter space Θ is finite. Finally the existence of a decision rule with the minimum R-ε risk is examined, when the risk set is closed from below and bounded.
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