Lower Bounds on Efficiency Ratios Based on Φ _p -Optimal Designs

Summary

Suppose that we intend to perform linear regression experiments with uncorrelated errors according to a given asymptotic design ξ. The problem which we address is the question of performance-stability of ξ under change of optimality criterion. More precisely, we describe a method of how to calculate lower bounds on the minimal possible efficiency of ξ with respect to any orthogonally invariant information function. The bounds constructed depend only on the eigenvalues of the information matrix of a known regular Φ _p -optimal 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.