Minimax nature of the linear estimates of the indefinite stochastic vector from the generalized probabilistic criteria

Consideration was given to the Bayesian estimation in the multidimensional indefinite-stochastic observation model using the minimax criterion with the generalized probabilistic risk functionals. The sufficient conditions for minimax-optimality of the linear estimate in the class of all measurable estimates were formulated. The cases of the risk functionals in the form of expected losses, the probabilities of error exaltation over some level, as well as the quantiles of the error norm were discussed in detail.