Optimal Design

Design of spatial experiments: Model fitting and prediction

“…The problem was extensively discussed (see for instance, Atkinson and Donev (1992), Fedorov (1972), Pazman (1986), Pukelsheim (1994) and Silvey (1980)), and it is difficult to add anything new in this area of experimental design theory. Theorem 1 which follows, is a generalized version of the Kiefer-Wolfowitz equivalence theorem, (see Kiefer (1959)) and stated here for the reader's convenience.…”

“…The choice of a sequence ,Os defines a variety of the algorithms; specific examples are given by Atkinson and Donev (1992), Cook and Nachtsheim (1989), Fedorov (1972Fedorov ( , 1975 and Silvey (1980). The following sequences are most popular:…”

Optimal discrimination designs for exponential regression models

“…Following Stigler (1971) and Studden (1982), who considered polynomial regression models, a reasonable approach to find optimal discrimination designs for this problem, is to use designs that are in some sense optimal for estimating the 2(k − s) parameters from the k − s highest terms in (1), to check if fitting these terms is actually necessary. An appropriate choice of optimality criterion is therefore the D 2(k−s) -criterion; see, e.g., Silvey (1980), i.e. we maximize the determinant of the matrix…”

“…, k − s, in the information matrix M k . From (5) it follows that the optimality criterion Φ(ξ, θ) belongs to the class of D A -optimality criteria; see, e.g., Silvey (1980), and is thus in some sense related to the D 2(k−s) -criterion for discriminating between η k and η s defined above. The Φ-optimal design is in this sense the D-optimal design for estimating the subset {a s+1 , .…”

Efficient experimental designs for sigmoidal growth models

“…In non-linear models the Fisher information matrix of the maximum likelihood estimator depends on the unknown parameters and for this reason optimal designs, which maximize some function of the Fisher information matrix are difficult to implement in practice. Many authors concentrate on local optimal designs, where it is assumed that a preliminary guess for the unknown parameters is available [see Chernoff (1953) or Silvey (1980)]. Most local optimal designs for non-linear regression models have been criticized for two reasons.…”