Geodesic
Asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 75-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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A quantitative estimate is given of the robustness of the characterization of the distribution with a density $a^{p/2}\Gamma(p/2)^{-1}|x|^{p-1}\exp-ax^2$ by the property of asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance with a quadratic loss function. 
@article{ZNSL_1976_61_a7,
     author = {L. B. Klebanov and I. A. Melamed},
     title = {Asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {75--83},
     year = {1976},
     volume = {61},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a7/}
}
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L. B. Klebanov; I. A. Melamed. Asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 75-83. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a7/