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By using the notion of a Haar ambivalent set introduced by Balka, Buczolichand Elekes (2012), essentially new classes of statistical structures havingobjective and strong objective estimates of unknown parameters are introducedin a Polish non-locally-compact group admitting an invariant metric andrelations between them are studied in this paper. An example of such a weaklyseparated statistical structure is constructed for which a question asking"{\it whether there exists a consistent estimate of an unknown parameter}" isnot solvable within the theory $(ZF)~\&~(DC)$. A question asking "{\it whetherthere exists an objective consistent estimate of an unknown parameter for anystatistical structure in a non-locally compact Polish group with an invariantmetric when subjective one exists}" is answered positively when there exists atleast one such a parameter the pre-image of which under this subjectiveestimate is a prevalent. These results extend recent results of authors. Someexamples of objective and strong objective consistent estimates in a compactPolish group $\{0; 1\}^N$ are considered in this paper.

journal of statistics : advances in theory and applications

On objective and strong objective consistent estimates of unknown  parameters for statistical structures in a Polish group admitting an  invariant metric