Some constructive results in guaranteed parameter estimation
The problem considered in this paper is the correlation-robust estimation of the parameters of linear regression models. Exact knowledge of the noise correlation matrix is not assumed. It is only assumed that some lower and upper bounds on the elements of this matrix are known. The problem treated is that of determining the linear unbiased estimate of regression parameters, which is optimal in a min-max sense. The max operation is on the class of covariance matrices satisfying the given lower and upper limitations; the min operation is on the class of linear transformations of the data, which produce unbiased estimates. Existence theorems as well as constructive results (for the particular case of location parameter estimation) are presented.
incomplete information about noise correlation
scientific article; zbMATH DE number 3896123