Geodesic
Low bounds for risk functions in non-parametric estimation problems
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 102-110

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The authors of the paper [1] have established some general minimax low bounds of risk functions for probability densities estimates, Here analogous results are proved for some other non-parametric estimation problems. 
@article{ZNSL_2011_396_a6,
     author = {I. A. Ibragimov},
     title = {Low bounds for risk functions in non-parametric estimation problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--110},
     publisher = {mathdoc},
     volume = {396},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a6/}
}
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I. A. Ibragimov. Low bounds for risk functions in non-parametric estimation problems. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 102-110. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a6/