Lower bounds on efficiency ratios based on Φp-optimal designs

Suppose that we intend to perform linear regression experiments with uncorrelated errors according to a given asymptotic design xi. The problem which we address is the question of performance-stability of xi under change of optimality criterion. More precisely, we describe a method of how to calculate lower bounds on the minimal possible efficiency of xi with respect to any orthogonally invariant information function. The bounds constructed depend only on the eigenvalues of the information matrix of a known regular Phi(p)-optimaJ design. We also point out some theoretical consequences of the bounds and illustrate the use of the results on the model of spring balance weighing.