Conservative Confidence Ellipsoids for Linear Model Parameters

This paper studies properties of conservative confidence ellipsoids for parameters of a general linear model. These regions are obtained on the basis of a linear estimator when only a vague knowledge of (heterogeneous) error variances is available. The required optimization problem is formulated and the solution space is described. The relationship of this problem to moments of quadratic forms in Gaussian random variables and to multiple hypergeometric functions is demonstrated. We explore the situation when the least favorable variances are equal. An example of a telephone switching study is considered.