Statistical Science

Gustav Elfving's contribution to the emergence of the optimal experimental design theory

J. Fellman

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Gustav Elfving contributed to the genesis of optimal experimental design theory with several papers mainly in the 1950s. These papers are presented and briefly analyzed. The connections between Elfving’s results and the results of his successors are elucidated to stress the relevance of Elfving’s impact on the development of optimal design theory.

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Statist. Sci., Volume 14, Number 2 (1999), 197-200.

First available in Project Euclid: 24 December 2001

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A-optimal designs As­optimal designs C­optimal designs optimality criteria relevant observations singularity


Fellman, J. Gustav Elfving's contribution to the emergence of the optimal experimental design theory. Statist. Sci. 14 (1999), no. 2, 197--200. doi:10.1214/ss/1009212245.

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  • Atkinson, A. C. and Donev, A. N. (1992). Optimum Experimental Designs. Clarendon, Oxford.
  • Chernoff, H. (1953). Locally optimal designs for estimating parameters. Ann. Math. Statist. 24 585-602. Dette, H. (1993a). Elfving's theorem for D-optimality. Ann. Statist. 21 753-766. Dette, H. (1993b). A new interpretation of optimality for Eoptimal designs in linear regression models. Metrika 40 37-50.
  • Dette, H., Heiligers, B. and Studden, W. J. (1995). Minimax designs in linear regression models. Ann. Statist. 23 30-40.
  • Dette, H. and Studden, W. J. (1993). Geometry of E-optimality. Ann. Statist. 21 416-433.
  • Elfving, G. (1952). Optimum allocation in linear regression theory. Ann. Math. Statist. 23 255-262.
  • Elfving, G. (1953). Convex sets in statistics. In Tolfte Skandinaviska Matematikerkongressen, Lund, August 10-15, 1953, 34-39. Elfving, G. (1954a). A unified approach to the allocation problem in sampling theory. Abstract from Proc. Inter. Math. Congr., Amsterdam, Sept. 1954. Elfving, G. (1954b). Geometric allocation theory. Skandinavisk Aktuarietidskrift 37 170-190.
  • Elfving, G. (1956). Selection of nonrepeatable observations for estimation. Proc. Third Berkeley Symp. Math. Statist. Probab. 1 69-75. Univ. California Press, Berkeley. Elfving, G. (1957a). A selection problem in experimental design. Societas Scientiarum Fennica Commentationes PhysicoMathematicae 20(2) 3-10. Elfving, G. (1957b). Minimax character of balanced experimental designs. In XIII Congr. Math. Scand. 69-76.
  • Elfving, G. (1959). Design of linear experiments. In Probability and Statistics: The Harald Cram´er Volume (U. Grenander, ed.) 58-74. Almquist and Wiksell, Stockholm.
  • Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
  • Fellman, J. (1974). On the allocation of linear observations. Societas Scientiarum Fennica Commentationes PhysicoMathematicae 44 27-78.
  • Fellman, J. (1980). On the behavior of the optimality criterion in the neighborhood of the optimal point. Working Paper 49, Swedish School of Economics and Business Administration.
  • Fellman, J. (1985). Topics on singular linear models with special reference to experimental design. In Proceedings of the First Tampere Seminar on Linear Models (1983) 101-122.
  • Fellman, J. (1991). Gustav Elfving and the emergence of the optimal design theory. Working Paper 218, Swedish School of Economics and Business Administration.
  • Fellman, J. (1997). Glimpses at the history of the statistical science in Finland. Theory of Stochastic Processes 3(19) 177- 182. (Proceedings of the Second Scandinavian-Ukrainian Conference in Mathematical Statistics, Ume a, 6-13 June 1997.)
  • Gaffke, N. (1985). Directional derivatives of optimality criteria at singular matrices in convex design theory. Statistics 16 373-388.
  • Karlin, S. and Studden, W. J. (1966). Optimal experimental designs. Ann. Math. Statist. 37 783-815.
  • Kiefer, J. (1959). Optimum experimental designs. J. Roy. Statist. Soc. Ser. B 21 272-319.
  • Kiefer, J. (1961). Optimum designs in regression problems, II. Ann. Math. Statist. 32 298-325.
  • Kiefer, J. (1962). Two more criteria equivalent to D-optimality of designs. Ann. Math. Statist. 33 792-796.
  • Kiefer, J. (1974). General equivalence theory for optimal designs (approximate theory). Ann. Statist. 2 849-879.
  • Kiefer, J. and Wolfowitz, J. (1959). Optimum designs in regression problems. Ann. Math. Statist. 30 271-294.
  • Kiefer, J. and Wolfowitz, J. (1960). The equivalence of two extremum problems. Canad. J. Math. 12 363-366.
  • Kiefer, J. and Wolfowitz, J. (1964). Optimum extrapolation and interpolation designs. I. Ann. Inst. Statist. Math. 16 79-108.
  • M¨akel¨ainen, T. (1990). Gustav Elfving 1908-1984. Address presented at the Gustav Elfving Meeting (organizer Ingram Olkin) at the International Workshop on Linear Models, Experimental Designs, and Related Matrix Theory, August 6-8, 1990, Tampere, Finland.
  • Nordstr ¨om, K. (1999). The life and work of Gustav Elfving. Statist. Sci. 14 174-196.
  • Pazman, A. (1986). Foundations of Optimum Experimental Design. Riedel, Dordrecht.
  • Pukelsheim, F. (1983). On optimality properties of simple block designs in the approximate design theory. J. Statist. Plann. Inference 8 193-208.
  • Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
  • Pukelsheim, F. and Titterington, D. M. (1983). General differential and Lagrangian theory for optimal experimental design. Ann. Statist. 11 1060-1068.
  • Silvey, S. D. (1978). Optimal design measures with singular information matrices. Biometrika 65 553-559.
  • Silvey, S. D. (1980). Optimal Design. Chapman and Hall, London.