Abstract Designs for quadratic and cubic regression are considered when the possible choices of the controlable variable are points x =( x 1 , x 2 ,…, x q ) in the q -dimensional. Full of radius R , B q ( R ) ={ x : Σ 4 i x 2 i ⩽ R 2 }. The designs that are optimum among rotatable designs with respect to the D -, A -, and E -optimality criteria are compared in their performance relative to these and other criteria, including extrapolation. Additionally, the performance of a design optimum for one value of R , when it is implemented for a different value of R , is investigated. Some of the results are developed algebraically; others, numerically. For example, in quadratic regression the A -optimum design appears to be fairly robust in its efficiency, under variation of criterion.
[1]
J. Kiefer.
Optimum Experimental Designs V, with Applications to Systematic and Rotatable Designs
,
1961
.
[2]
J. Kiefer.
Optimum Experimental Designs
,
1959
.
[3]
J. Kiefer.
General Equivalence Theory for Optimum Designs (Approximate Theory)
,
1974
.
[4]
J. Kiefer,et al.
The Equivalence of Two Extremum Problems
,
1960,
Canadian Journal of Mathematics.
[5]
W. J. Studden,et al.
Optimal Designs for Large Degree Polynomial Regression
,
1976
.
[6]
W. J. Studden,et al.
Theory Of Optimal Experiments
,
1972
.
[7]
J. Kiefer.
Optimal design: Variation in structure and performance under change of criterion
,
1975
.