Geodesic
More on the estimation of distribution densities
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part V, Tome 108 (1981), pp. 72-88

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This paper improves some results on the rate of decrease of minimax risk for nonparametric density estimators which have been proved in the previous work of the authors [2]. For example, we prove that $\inf_n\inf_{f_n^*}\sup_f\|f-f_n^*\|_1>1$ even if the density function $f$ belongs to the class of entire functions of exponential type $\Lambda$ ($\Lambda$ is known). 
@article{ZNSL_1981_108_a5,
     author = {I. A. Ibragimov and R. Z. Khas'minskii},
     title = {More on the estimation of distribution densities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--88},
     publisher = {mathdoc},
     volume = {108},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a5/}
}
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I. A. Ibragimov; R. Z. Khas'minskii. More on the estimation of distribution densities. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part V, Tome 108 (1981), pp. 72-88. http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a5/