Prior to the 1970's a substantial literature had accumulated on the
theory of optimal design, particularly of optimal linear regression
design. To a certain extent the study of the subject had been piecemeal,
different criteria of optimality having been studied separately. Also to
a certain extent the topic was regarded as being largely of theoretical
interest and as having little value for the practising statistician.
However during this decade two significant developments occurred. It was
observed that the various different optimality criteria had several
mathematical properties in common; and general algorithms for
constructing optimal design measures were developed. From the first of
these there emerged a general theory of remarkable simplicity and the
second at least raised the possibility that the theory would have more
practical value. With respect to the second point there does remain a
limiting factor as far as designs that are optimal for parameter
estimation are concerned, and this is that the theory assumes that the
model be collected is known a priori. This of course underlying data to
is seldom the case in practice and it often happens that designs which
are optimal for parameter estimation allow no possibility of model
validation. For this reason the theory of design for parameter
estimation may well have to be combined with a theory of model
validation before its practical potential is fully realized.
Nevertheless discussion in this monograph is limited to the theory of
design optimal for parameter estimation.