The Families with a “Universal” Location Estimator
The problem of estimating the multidimensional location parameter is considered. The new family of multivariate distribution is characterized by the property of the independence of the best equivariant estimator on the even loss function choice. Some generalizations of known functional equations are introduced and solved for this aim.
Key WordsMultidimensional location parameter loss function equivariant estimators completely symmetrical families D’Alembert’s functional equation
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