Asymptotic $\varepsilon$-admissibility of the sample variance as an estimator of the population variance

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.