Geodesic
The boundaries of risk in the problem of estimation of symmetrical distributions
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part IV, Tome 98 (1980), pp. 98-114

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The modification of nonparametric information inequalities under the available additional information about the infinitedimentional estimated parameter, obtaind in [1], is considered. The common constructions are motived, in parfcicular, by the problems of estimation of distribution functions, which are invariant respect to different groups of transformations in $R^k$. 
@article{ZNSL_1980_98_a8,
     author = {Yu. A. Koshevnik and B. Ya. Levit},
     title = {The boundaries of risk in the problem of estimation of symmetrical distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--114},
     publisher = {mathdoc},
     volume = {98},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_98_a8/}
}
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Yu. A. Koshevnik; B. Ya. Levit. The boundaries of risk in the problem of estimation of symmetrical distributions. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part IV, Tome 98 (1980), pp. 98-114. http://geodesic.mathdoc.fr/item/ZNSL_1980_98_a8/