Geodesic
When has a~quadratic statistics a~constant regression on the sample mean?
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 646-648

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Let $x_1,\dots,x_n$ be independent identically distributed non-degenerate random variables with finite second moment. Let $Q$ be a quadratic statistics with real coefficients and $\Lambda=x_1+\dots+x_n$. The condition $\mathbf E(Q\mid\Lambda)=\mathbf EQ$ is studied. 
@article{TVP_1979_24_3_a23,
     author = {L. B. Klebanov},
     title = {When has a~quadratic statistics a~constant regression on the sample mean?},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {646--648},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a23/}
}
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L. B. Klebanov. When has a~quadratic statistics a~constant regression on the sample mean?. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 646-648. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a23/