Article

Acta Applicandae Mathematica

, Volume 43, Issue 1, pp 17-42

Spectral methods in linear minimax estimation

  • Hilmar DrygasAffiliated withDepartment of Mathematics, University of Kassel

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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.

Mathematics Subject Classification (1991)

62J05

Key words

linear minimax estimation Bayesian approach spectral methods spectral equations Hoffmann-Laüter representation