Open Access
October, 1969 Optimal and Efficient Designs of Experiments
Corwin L. Atwood
Ann. Math. Statist. 40(5): 1570-1602 (October, 1969). DOI: 10.1214/aoms/1177697374


This paper consists of new results continuing the series of papers on optimal design theory by Kiefer (1959), (1960), (1961), Kiefer and Wolfowitz (1959), (1960), Farrell, Kiefer and Walbran (1965) and Karlin and Studden (1966a). After disposing of the necessary preliminaries in Section 1, we show in Section 2 that in several classes of problems an optimal design for estimating all the parameters is supported only on certain points of symmetry. This is applied to the problem (introduced by Scheffe (1958)) of multilinear regression on the simplex. In Section 3 we consider optimality when nuisance parameters are present. A new sufficient condition for optimality is given. A corrected version is given to the condition which Karlin and Studden (1966a) state as equivalent to optimality, and we prove the natural invariance theorem involving this condition. These results are applied to the problem of multilinear regression on the simplex when estimating only some of the parameters. Section 4 consists primarily of a number of bounds on the efficiency of designs; these are summarized at the beginning of that section.


Download Citation

Corwin L. Atwood. "Optimal and Efficient Designs of Experiments." Ann. Math. Statist. 40 (5) 1570 - 1602, October, 1969.


Published: October, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0182.51905
MathSciNet: MR260119
Digital Object Identifier: 10.1214/aoms/1177697374

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 5 • October, 1969
Back to Top