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DETERMINANT FORMULAS WITH APPLICATIONS TO

DESIGNING WHEN THE OBSERVATIONS ARE CORRELATED

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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.

**Source**
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