We present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.
"Information-theoretic determination of minimax rates of convergence." Ann. Statist. 27 (5) 1564 - 1599, October 1999. https://doi.org/10.1214/aos/1017939142