MINIMAX NONPARAMETRIC-ESTIMATION

Let Y be a random variable (or vector) taking its values in some measurable space and having the completely unknown distribution P. Further, let Z1, Z2, ...., Z(r) be the real valued functions defined on the same space. We find the minimax estimator d-degrees of the expected value of (Z1(Y), Z2(Y), ..., Z(r)(Y)) with respect to the generalized quadratic errors loss function. We also show that d-degrees remains minimax when the class of all possible distributions of Y is restricted to a sufficiently ''rich'' subset of all discrete distributions.