Consideration was given to the minimax estimation in the observation system including a hidden Markov model for continuous and counting observations. The dynamic and observation equations depend on a random finite-dimensional parameter having an unknown distribution with the given support. The conditional expectation of the available observation of some generalized quadratic loss function was used as the risk function. Existence of the saddle point in the formulated minimax problem was proved, and the worst distribution and the minimax estimate as the solution of a simpler dual problem were characterized.
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Original Russian Text © A. V. Borisov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 11, pp. 31–45.
This work was supported by the Russian Foundation for Basic Research, project no. 05-01-00508-a, and the Program for Fundamental Algorithms of Information Technologies of the Department of Information Technologies and Computer Systems, Russian Academy of Sciences.
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Borisov, A.V. Minimax a posteriori estimation in the hidden Markov models. Autom Remote Control 68, 1917–1930 (2007). https://doi.org/10.1134/S0005117907110033