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A posteriori minimax estimation with likelihood constraints


Consideration was given to the problem of guaranteed estimation of the parameters of an uncertain stochastic regression. The loss function is the conditional mean squared error relative to the available observations. The uncertainty set is a subset of the probabilistic distributions lumped on a certain compact with additional linear constraints generated by the likelihood function. Solution of this estimation problem comes to determining the saddle point defining both the minimax estimator and the set of the corresponding worst distributions. The saddle point is the solution of a simpler finite-dimensional dual optimization problem. A numerical algorithm to solve this problem was presented, and its precision was determined. Model examples demonstrated the impact of the additional likelihood constraints on the estimation performance.

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Correspondence to A. V. Borisov.

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Original Russian Text © A.V. Borisov, 2012, published in Avtomatika i Telemekhanika, 2012, No. 9, pp. 49–71.

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Borisov, A.V. A posteriori minimax estimation with likelihood constraints. Autom Remote Control 73, 1481–1497 (2012).

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  • Saddle Point
  • Remote Control
  • Loss Function
  • Dual Problem
  • Conditional Expectation