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In statistical theory one comes across various families of statistics (subfields). For each such family, it is of some interest to ask oneself as to whether the family has maximal and/or minimal elements. The author proves here the existence of such elements in a number of cases and leaves the question unsolved in a number of other cases. A number of problems of an allied nature are also discussed.

Problems Relating to the Existence of Maximal and Minimal Elements in Some Families of Statistics (Subfields)