On a class of algorithms from experimental design theory
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 24 (1-2) , 91-126
- https://doi.org/10.1080/02331939208843782
Abstract
The theory of optimal (approximate) linear regression design has produced several iterative methods to solve a special type of convex minimization problems. The present paper gives a unified and extended theoretical treatment of the methods. The emphasis is on the mathematical structures relevant for the optimization process, rather than on the statistical background of experimental design. So the main body of the paper can be read independently from the experimental design context. Applications are given to a special class of extremum problems arising in statistics. The numerical results obtained indicate that the methods are of practical interestKeywords
This publication has 22 references indexed in Scilit:
- An empirical study of a class of iterative searches for optimal designsJournal of Statistical Planning and Inference, 1989
- A vertex-exchange-method in D-optimal design theoryMetrika, 1986
- A remark on the numerical estimation of probabilitiesStatistics, 1986
- Numerical estimation of a probability measureJournal of Statistical Planning and Inference, 1985
- Directional derivatives of optimality criteria at singular matrices in convex design theoryStatistics, 1985
- Numerical techniques for estimating probabilitiesJournal of Statistical Computation and Simulation, 1982
- Convergent Design Sequences, for Sufficiently Regular Optimality Criteria, II: Singular CaseThe Annals of Statistics, 1980
- Convergent Design Sequences, for Sufficiently Regular Optimality CriteriaThe Annals of Statistics, 1976
- Sequences Converging to $D$-Optimal Designs of ExperimentsThe Annals of Statistics, 1973
- Optimal and Efficient Designs of ExperimentsThe Annals of Mathematical Statistics, 1969