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Some incomplete but boundedly complete location families. (English) Zbl 0790.62016

Summary: A general result concerning noncompleteness of location families of probability measures on Euclidean space is pointed out. Examples include boundedly complete families, such as those generated by certain scale mixtures of the standard Gaussian distribution. These examples illuminate completeness criteria for location families and compare favourably in simplicity with previously known examples of incomplete boundedly complete (nonlocation) families.

MSC:

62B99 Sufficiency and information
62F10 Point estimation
44A35 Convolution as an integral transform
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