More on the estimation of distribution densities

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).