arXiv 1502.074632015-02math.STstat.TH

关于容许不变度量的波兰群中统计结构未知参数的客观和强客观相合估计

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

Murman Kintsurashvili, Tengiz Kiria, Gogi Pantsulaia

备注：: 40 pages, 3 figures. In Table 1 (p.4) last column is deleted; In Page 28, indications of Statistics $T_n^{(1)}$(and $T_n^{(3)}$ are corrected ((5.14) is replaced with (5.13); (5.30) is replaced with (5.19); P. 29, line 5,1 from above $T^{(1)}_ n$ is replaced with $T^{(2)}_ n$; The corresponding correction is entered in Table 2. AoS is deleted . Now pages are 34
发表信息：: Journal of Statistics: Advances in Theory and Applications, Volume 13, No. 2 (2015) 179-233
DOI：: 10.18642/jsata_7100121469

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摘要：

利用Haar矛盾集的概念，在具有不变度量的波兰非局部紧群中引入了一类新的统计结构，并研究了它们之间的关系.这样一个弱分离的统计结构的一个例子是构造一个问题，问“{ \it是否存在一个相合估计未知参数}”是不能解决的理论$(ZF)~\&~(DC)$内。一个问题，问“{ \it是否存在一个客观的相合估计的任何统计结构中的一个非局部紧凑的波兰组不变的度量时，主观的存在}”是肯定的回答时，存在至少一个这样的参数，在这个主观估计的前图像是普遍的。这些结果推广了作者最近的结果。本文考虑了紧波兰群$\{0; 1\}^N$中客观和强客观相合估计的一些例子.

英文摘要：

By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), 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 "{\it whether there exists a consistent estimate of an unknown parameter}" is not solvable within the theory $(ZF)~\&~(DC)$. A question asking "{\it 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 $\{0; 1\}^N$ are considered in this paper.

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