Experiments for Nonlinear Functions (R.A. Fisher Memorial Lecture)

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Abstract
This article reviews work on the planning of experiments with response functions nonlinear in some parameters. Apart from older work on dilution series experiments and quantal bioassays, this field is relatively recent, the mathematical and computing aspects being more complex than for linear responses. An efficient design requires good advance estimates of the parameters. Research has concentrated on (1) optimum estimation of the parameters, under an asymptotic criterion, for both sequential and non-sequential approaches, and (2) tests of the adequacy of the model, discrimination between models and model-building. More work on the small-sample behavior of the designs and on compromise designs that perform well under the typical practical complications would be valuable.