, Volume 43, Issue 1, pp 17-42

Spectral methods in linear minimax estimation

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Abstract

We consider the minimax-linear estimator in a linear regression model with circular constraints. Two necessary and sufficient conditions for the optimality of an estimator, the socalled left spectral equation and the right spectral equation (Girko spectral equation), are derived. For the special case of a simple maximal eigenvalue and a single eigenspace explicit estimation formulas are derived. These formulas also show some of the shortcomings of the minimax-linear estimator (MILE). Finally, the relation with Bayesian analysis and the Hoffmann-Läuter estimator is outlined.