Geodesic
More on the estimation of distribution densities
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part V, Tome 108 (1981), pp. 72-88 
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/
@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},
     year = {1981},
     volume = {108},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a5/}
}
TY  - JOUR
AU  - I. A. Ibragimov
AU  - R. Z. Khas'minskii
TI  - More on the estimation of distribution densities
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1981
SP  - 72
EP  - 88
VL  - 108
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a5/
LA  - ru
ID  - ZNSL_1981_108_a5
ER  - 
%0 Journal Article
%A I. A. Ibragimov
%A R. Z. Khas'minskii
%T More on the estimation of distribution densities
%J Zapiski Nauchnykh Seminarov POMI
%D 1981
%P 72-88
%V 108
%U http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a5/
%G ru
%F ZNSL_1981_108_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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).