Geodesic
Bayesian estimates, stable with respect to the choice of the loss function
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 327-334.

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A family of distributions is defined for which the generalized Bayesian estimate of a real parameter $\theta$, constructed according to the repeated choice, does not depend on the choice of the even convex loss function from a sufficiently wide class. It is shown that these families are a subclass of the exponential families with a sufficient statistic for the parameter $\theta$ of rank two. 
@article{MZM_1978_23_2_a16,
     author = {L. B. Klebanov},
     title = {Bayesian estimates, stable with respect to the choice of the loss function},
     journal = {Matemati\v{c}eskie zametki},
     pages = {327--334},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a16/}
}
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L. B. Klebanov. Bayesian estimates, stable with respect to the choice of the loss function. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 327-334. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a16/