Experimental design in a class of models

Abstract

Let there be a set F of mathematical models L _m(x) for the description of the depend once of a real random variable y(x) on , where m is an element of a subscript set M which may be continuous. Let . We suppose that the models are linearly dependent on the parameters. The observation errors ε(x) may be uncorrelated for different measurements, and . The problem is to find an experimental design which enables us to find the best possible estimate of the parameters for all models of F. Therefore the following criteria are used: For a measure Q, on a σ algebra of M we consider the functionals and

where is the determinant of the information matrix of the model L _m for the continuous design ξ. Properties of designs maximizing C(ξ) and S(ξ) are given. For instance a minimax property, and iterative computing procedures for C and S-optimal estimation and discrimination problems can be treated using the given method. A relationship to the results of S.M. STIGLER (1971) and A.C. ATKINSON (1972) is also indicated.