Geodesic
Non-parametric estimation of a nonlinear functional of regression in case of the given plan
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 143-154

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bower bound of estimation quality is found. An estimator asymptotically achieving this bound is constructed. 
@article{ZNSL_1988_166_a15,
     author = {Yu. I. Pastukhova},
     title = {Non-parametric estimation of a nonlinear functional of regression in case of the given plan},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {143--154},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a15/}
}
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Yu. I. Pastukhova. Non-parametric estimation of a nonlinear functional of regression in case of the given plan. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 143-154. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a15/