Abstract: | Minimax nonhomogeneous linear estimators of scalar linear parameter functions are studied in the paper under restrictions
on the parameters and variance-covariance matrix. The variance-covariance matrix of the linear model under consideration is
assumed to be unknown but from a specific set R of nonnegativedefinite matrices. It is shown under this assumption that, without
any restriction on the parameters, minimax estimators correspond to the least-squares estimators of the parameter functions
for the “worst” variance-covariance matrix. Then the minimax mean-square error of the estimator is derived using the Bayes
approach, and finally the exact formulas are derived for the calculation of minimax estimators under elliptical restrictions
on the parameter space and for two special classes of possible variance-covariance matrices R. For example, it is shown that
a special choice of a constant q
0
and a matrixW
0 defining one of the above classes R leads to the well known Kuks—Olman admissible estimator (see 16]) with a known variance-covariance
matrixW
0. Bibliography:32 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 79–92. |