DETERMINANT FORMULAS WITH APPLICATIONS TO DESIGNING WHEN THE OBSERVATIONS ARE CORRELATED

WOLFGANG BISCHOFF

Institute of Mathematical Stochastics, Department of Mathematics, University of Karlsruhe, D-76128 Karlsruhe, Germany

(Received June 13, 1994; revised December 5, 1994)

Abstract. In the general linear model consider the designing problem for the Gauß-Markov estimator or for the least squares estimator when the observations are correlated. Determinant formulas are proved being useful for the D-criterion. They allow, for example, a (nearly) elementary proof and a generalization of recent results for an important linear model with multiple response. In the second part of the paper the determinant formulas are used for deriving lower bounds for the efficiency of a design. These bounds are applied in examples for tridiagonal covariance matrices. For these examples maximin designs are determined.

Key words and phrases: Determinant formula, general linear model, correlated observations, D-criterion, efficiency of designs, linear model with multiple response, lower bounds for the efficiency, tridiagonal matrices as covariance structure, maximin designs.