On a class of algorithms from experimental design theory

References

• Atwood , C.L. 1969 . Optimal and efficient designs of experiments . Ann. Math. Statist , 40 : 1570 – 1602 .
   Google Scholar
• Atwood , C.L. 1973 . Sequences converging to D-optimal designs of experiments . Ann. Statist , 1 : 342 – 352 .
   Web of Science ®Google Scholar
• Atwood , C.L. 1976 . Convergent design sequences, for sufficiently regular optimality criteria . Ann. Statist , 4 : 1124 – 1138 .
   Web of Science ®Google Scholar
• Atwood , C.L. 1980 . Convergent design sequences, for sufficiently regular optimality criteria, II: Singular case . Ann. Statist , 8 : 894 – 912 .
   Google Scholar
• Böhning , D. 1985 . Numerical estimation of a probability measure . J. Statist. Plann. Inference , 11 : 57 – 69 .
   Web of Science ®Google Scholar
• Böhning , D. 1986 . A vertex-exchange-method in D-optimal design theory . Metrika , 33 : 337 – 347 .
   Google Scholar
• Böhning , D. 1982 . Numerical techniques for estimating probabilities . J. Statist. Comp. Simula , 14 : 283 – 293 .
   Web of Science ®Google Scholar
• Böhning , D. and Hoffmann , K.H. 1986 . A remark on the numerical estimation of probabilities . Statistics , 17 : 231 – 236 .
   Google Scholar
• Fedorov , V.V. 1972 . Theory of Optimal Experiments , New York : Academic Press .
   Google Scholar
• Fellman , J. 1989 . An empirical study of a class of iterative searches for optimal designs . J. Statist. Plann. Inference , 21 : 85 – 92 .
   Web of Science ®Google Scholar
• Gaffke , N. 1985 . Directional derivatives of optimality criteria at singular matrices in convex design theory . Statistics , 16 : 373 – 388 .
   Google Scholar
• Gaffke , N. and Heiligers , B. 1989 . Bayes, admissible, and minimax linear estimators in linear models with restricted parameter space . Statistics , 20 : 487 – 508 .
   Google Scholar
• Gaffke , N. and Mathar , R. . Linear minimax estimation and related Bayes L-optimal design. Methods of Operations Research 60 . Proceedings XIII. Symposium on Operations Research 1988 . pp. 617 – 628 .
   Google Scholar
• Higgins , J.E. and Polak , E. 1990 . Minimizing pseudoconvex functions on convex compact sets . Journal of Optimization Theory and Applications , 65 : 1 – 27 .
   Web of Science ®Google Scholar
• McCormick , G.P. 1983 . Nonlinear Programming , New York : John Wiley & Sons .
   Google Scholar
• Ortega , J.M. and Rheinboldt , W.C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
   Google Scholar
• pázman , A. 1986 . Foundations of Optimum Experimental Design , Dordrecht : Reidel Publishing .
   Google Scholar
• Pilz , J. 1986 . Minimax linear regression estimation with symmetric parameter restrictions . J. Statist. Plann. inference , 13 : 297 – 318 .
   Web of Science ®Google Scholar
• Pukelsheim , F. 1980 . On linear regression design which maximize information . J. Statist. Plann. Inference , 4 : 339 – 364 .
   Web of Science ®Google Scholar
• Pukelsheim , F. and Styan , G.P.H. 1983 . Convexity and monotonicity properties of dispersion matrices of estimators in linear models . Scand. J. Statist , 10 : 145 – 149 .
   Google Scholar
• Rieder , S. 1990 . “ Versuchspläne mit vorgegebenen Trägerpunkten ” . Universität Augsburg . (In German). Diplom Thesis, Institut für Mathematik
   Google Scholar
• Rockafellar , R.T. 1970 . Convex Analysis Princeton
   Google Scholar
• Silvey , S.D. , Titterington , D.M. and Torsney , B. 1978 . An algorithm for optimal design on a finite design space . Comm. Statist.-Theor. Meth , A7 ( 14 ) : 1379 – 1389 .
   Web of Science ®Google Scholar
• Stahlecker , P. and Lauterbach , J. 1987 . Approximate minimax estimation in linear regression: Theoretical results . Comm. Statist.-Theor. Meth , 16 ( 4 ) : 1101 – 1116 .
   Web of Science ®Google Scholar
• Titterington , D.M. . Algorithms for computing D-optimal designs on a finite design space . Proc. 1976 Conf. on Info-Science and Systems . pp. 213 – 216 .
   Google Scholar
• Torsney , B. 1988 . “ Computing optimizing distributions with applications in design, estimation and image processing ” . In Optimal Design and Analysis of Experiments , Edited by: Dodge , Y. , Fedorov , V.V. and Wynn , H.P. 361 – 370 . Amsterdam : Elsevier .
   Google Scholar
• Wu , C.F. 1978a . Some algorithmic aspects of the theory of optimal designs . Ann. Statist , 6 : 1286 – 1301 .
   Web of Science ®Google Scholar
• Wu , C.F. 1978b . Some iterative procedures for generating nonsingular optimal designs . Comm. Statist.-Theor. Meth , A7 ( 14 ) : 1399 – 1412 .
   Web of Science ®Google Scholar
• Wu , C.F. 1978 . The convergence of general step-length algorithms for regular optimum design criteria . Ann. Statist , 6 ( 14 ) : 1273 – 1285 .
   Web of Science ®Google Scholar
• Wynn , H.P. 1970 . The sequential generation of D-optimum experimental designs . Ann. Math. Statist , 41 ( 14 ) : 1655 – 1664 .
   Google Scholar
• Wynn , H.P. 1972 . Results in the theory and construction of D-optimum experimental designs . Roy. Statist. Soc. Ser.B , 34 ( 14 ) : 133 – 147 .
   Google Scholar