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This paper derives robust minimax estimators for a class of uncertain models. The uncertainty is described by a relative entropy constraint between the unknown joint distribution and a fixed nominal joint distribution. The maximization is addressed using variational methods, while the minimization is addressed using the concept of a sufficient statistic, which is an unnormalized version of the a posteriori density. The theory developed is applied to multipath fading wireless channels, to derive minimax envelope and phase estimates. Related results are also derived when the uncertainty shrinks to zero.