On the problem of the minimal sample size for the ratio estimation: an Empirical Bayes approach

In many application contexts it may be useful to adopt a measure of precision for the estimation of the proportion \uf070 of units belonging to a certain population having some definite characteristics taking into account the value of this unknown fraction. This work discusses the use of objective prior information, deriving from pre-test or pilot inquires, and the application of Empirical Bayes Procedures in the context of experimental sample design when there is the need for the definition of the minimal sufficient sampling size required to grant the desidered relative precision