Abstract:  The problem of minimax-optimal estimation in the multivariate uncertain-stochastic observation model is studied by means of generalized probabilistic risk functions. The most general results in this area have been obtained by using the mean-square risk. Nevertheless, the statistical references based on the mean-square error can lead to non-adequate decisions if the exact joint distribution of random parameters differs from the Gaussian law. At the same time, given a priori statistical information in terms of restrictions on the moment characteristics, one can find the tight bounds of various non-mean-square risk functions at linear decision rules. This makes possible to suggest efficient optimization procedures for designing linear estimation algorithms, which are optimal in a minimax sense. The practical and theoretical interests motivate to put the following question: whether linear estimators are minimax-optimal over the class of all measurable decision rules given fixed second-order moments of random parameters? For various linear uncertain-stochastic systems this problem has been investigated in detail by using the mean-square risk. The main goal of this talk is to show the optimality of linear estimates for a broad class of probabilistic risk functions. This result is illustrated by means of several examples based on the expectation, probability, and quantile functions.