Mattner, L. Some incomplete but boundedly complete location families. (English) Zbl 0790.62016 Ann. Stat. 21, No. 4, 2158-2162 (1993). 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. Cited in 17 Documents MSC: 62B99 Sufficiency and information 62F10 Point estimation 44A35 Convolution as an integral transform Keywords:bounded completeness; characteristic function; Fourier transform; injectivity of convolution; noncompleteness of location families; Euclidean space; boundedly complete families; scale mixtures; Gaussian distribution; completeness criteria; location families × Cite Format Result Cite Review PDF Full Text: DOI