The asymptotic minimax constant for sup-norm loss in nonparametric densityestimation

We develop the exact constant of the risk asymptotics in the uniform norm f or density estimation. This constant has already been found for nonparametr ic regression and for signal estimation in Gaussian white noise. Holder cla sses for arbitrary smoothness index beta>0 on the unit interval are conside red. The constant involves the value of an optimal recovery problem as in t he white noise case, but in addition it depends on the maximum of densities in the function class.