Volume no :13, Issue no: 2, June (2015)

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

Author's: Murman Kintsurashvili, Tengiz Kiria and Gogi Pantsulaia
Pages: [179] - [233]
Received Date: March 19, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121469

Abstract

By using the notion of a Haar ambivalent set introduced by Balka et al. [1], essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a Polish non-locally-compact group admitting an invariant metric and relations between them are studied in this paper. An example of such a weakly separated statistical structure is constructed for which a question asking “whether there exists a consistent estimate of an unknown parameter” is not solvable within the theory (ZF) & (DC). A question asking “whether there exists an objective consistent estimate of an unknown parameter for any statistical structure in a non-locally compact Polish group with an invariant metric when subjective one exists” is answered positively when there exists at least one such a parameter the pre-image of which under this subjective estimate is a prevalent. These results extend recent results of authors. Some examples of objective and strong objective consistent estimates in a compact Polish group are considered in this paper.

Keywords

an objective infinite-sample consistent estimate, shy set, Haar ambivalent set, Polish group.