Geodesic
$L_k^{(2)}$-sufficient subspaces for families with shift and scale parameters
Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 279-291.

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In the paper we describe $L_k^{(2)}$-sufficient subspaces of dimension $k+1$ for the families mentioned in the title. We give necessary conditions for the presence of these subspaces, expressed in terms of the moments of a distribution function. 
@article{MZM_1976_20_2_a13,
     author = {L. B. Klebanov},
     title = {$L_k^{(2)}$-sufficient subspaces for families with shift and scale parameters},
     journal = {Matemati\v{c}eskie zametki},
     pages = {279--291},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a13/}
}
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L. B. Klebanov. $L_k^{(2)}$-sufficient subspaces for families with shift and scale parameters. Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 279-291. http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a13/