Minimax estimation for singular linear multivariate models with mixed uncertainty

Authors:
Alexei R. Pankov;Konstantin V. Siemenikhin
Affiliations:
Probability Theory Department, Moscow Aviation Institute, Volokolamskoye shosse, Moscow, Russia;Probability Theory Department, Moscow Aviation Institute, Volokolamskoye shosse, Moscow, Russia
Venue:
Journal of Multivariate Analysis
Year:
2007

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Abstract

The problem of minimax estimation is examined for the linear multivariate statistically indeterminate observation model with mixed uncertainty. The a priori information on the distributions of model parameters is formulated in terms of second-order moment characteristics. It is shown that in the regular case the minimax estimate is defined explicitly via the solution of the dual optimization problem. For singular models, the method of dual optimization is developed by means of using the Tikhonov regularization techniques. Several particular cases which are widely used in practice are also considered.