Optimal designs and large-sample tests for linear hypotheses

Abstract

Moment conditions beyond those required for Gauss-Markov estimation are shown to yield error bounds on normal-theory approximations to type I error probabilities and confidence coefficients associated with variance ratio tests, Scheffé's (1953) bounds, and Dunnett's (1955) procedure for comparing k treatments with a control. These bounds depend on the experimental design. The error-minimizing designs are characterized and shown to be orthogonal.