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Variational theorems in gnostical theory of uncertain data. (English) Zbl 0873.62004
Summary: Main objection of any theory dealing with estimation is to find “good” estimators. But how to justify that estimators derived by means of the theory are really good? One of the most popular methods is to choose estimators according to some optimality principle. Examples of optimality principles commonly used in statistics are maximum likelihood principle or minimum distance principle.
Gnostical theory of uncertain data (GT) is a new approach to the processing of data influenced by uncertainty. For GT, as for any theory of data processing, the problem of characterizing optimality principles leading to estimators is of primary interest. Solving this problem is the main topic of this paper. The optimality principles are formulated as specific variational theorems.
MSC:
62A01 Foundations and philosophical topics in statistics
62B10 Statistical aspects of information-theoretic topics
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