Geodesic
An $\varepsilon$-admissibility condition on the sample mean as an estimator of a location parameter in the presence of a nuisance scale parameter
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 25-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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An estimate of stability is obtained in a theorem on characterizing the normal law by the property of sufficiency of the sample mean as an estimate of the location parameter in the presence of a nuisance scale parameter when the loss function is quadratic. 
@article{ZNSL_1976_61_a2,
     author = {A. A. Zinger},
     title = {An $\varepsilon$-admissibility condition on the sample mean as an estimator of a location parameter in the presence of a nuisance scale parameter},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {25--37},
     year = {1976},
     volume = {61},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a2/}
}
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A. A. Zinger. An $\varepsilon$-admissibility condition on the sample mean as an estimator of a location parameter in the presence of a nuisance scale parameter. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 25-37. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a2/