Optimal rates of entropy estimation over Lipschitz balls
Optimal rates of entropy estimation over Lipschitz balls
We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates $(n\ln n)^{-s/(s+d)}+n^{-1/2}$ for $0<s\leq 2$ for densities supported on $[0,1]^{d}$, where $s$ is the smoothness parameter and …