Minimax redundancy through accumulated estimation error

Minimax expected redundancies over memoryless source classes of smooth densities are studied, through their connections with accumulated prediction errors and using available techniques from nonparametric statistics. To derive lower bounds on the minimax expected redundancy rates, two methods are used and compared. One is the Assouad´s technique from statistical density estimation and the other is the information-theoretic (generalized) Fano´s inequality. Both methods are applied to hypercube sub-classes and a connection between Assouad´s and Fano´s is established using a packing number result from error-correcting coding theory. Finally, optimal (rate) codes, which achieve the minimax rate lower bounds on expected redundancy, are formed based on optimal density estimators