Gustav Elfving's contribution to the emergence of the optimal experimental design theory
J. Fellman
Source: Statist. Sci. Volume 14, Number 2
(1999), 197-200.
Abstract
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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Keywords: A-optimal designs; Asoptimal designs; Coptimal designs; optimality criteria; relevant observations; singularity
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Permanent link to this document: http://projecteuclid.org/euclid.ss/1009212245
Mathematical Reviews number (MathSciNet): MR1722070
Digital Object Identifier: doi:10.1214/ss/1009212245
Zentralblatt MATH identifier: 02068901
References
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.
Mathematical Reviews (MathSciNet): MR15,452j
Zentralblatt MATH: 0053.10504
Digital Object Identifier: doi:10.1214/aoms/1177728915
Project Euclid: euclid.aoms/1177728915
Dette, H., Heiligers, B. and Studden, W. J. (1995). Minimax designs in linear regression models. Ann. Statist. 23 30-40.
Mathematical Reviews (MathSciNet): MR96b:62119
Zentralblatt MATH: 0847.62063
Digital Object Identifier: doi:10.1214/aos/1176324453
Project Euclid: euclid.aos/1176324453
Dette, H. and Studden, W. J. (1993). Geometry of E-optimality. Ann. Statist. 21 416-433.
Mathematical Reviews (MathSciNet): MR94g:62150
Zentralblatt MATH: 0780.62057
Digital Object Identifier: doi:10.1214/aos/1176349034
Project Euclid: euclid.aos/1176349034
Elfving, G. (1952). Optimum allocation in linear regression theory. Ann. Math. Statist. 23 255-262.
Mathematical Reviews (MathSciNet): MR13,963h
Zentralblatt MATH: 0047.13403
Digital Object Identifier: doi:10.1214/aoms/1177729442
Project Euclid: euclid.aoms/1177729442
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.
Mathematical Reviews (MathSciNet): MR65884
Zentralblatt MATH: 0056.37201
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.
Mathematical Reviews (MathSciNet): MR18,946d
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.
Mathematical Reviews (MathSciNet): MR22:1970
Zentralblatt MATH: 0119.35202
Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
Mathematical Reviews (MathSciNet): MR53:6916
Zentralblatt MATH: 0261.62002
Fellman, J. (1974). On the allocation of linear observations. Societas Scientiarum Fennica Commentationes PhysicoMathematicae 44 27-78.
Mathematical Reviews (MathSciNet): MR50:8839
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.
Mathematical Reviews (MathSciNet): MR86k:62122
Digital Object Identifier: doi:10.1080/02331888508801868
Karlin, S. and Studden, W. J. (1966). Optimal experimental designs. Ann. Math. Statist. 37 783-815.
Mathematical Reviews (MathSciNet): MR33:5055
Zentralblatt MATH: 0151.23904
Digital Object Identifier: doi:10.1214/aoms/1177699361
Project Euclid: euclid.aoms/1177699361
Kiefer, J. (1959). Optimum experimental designs. J. Roy. Statist. Soc. Ser. B 21 272-319.
Mathematical Reviews (MathSciNet): MR22:4101
JSTOR: links.jstor.org
Kiefer, J. (1961). Optimum designs in regression problems, II. Ann. Math. Statist. 32 298-325.
Mathematical Reviews (MathSciNet): MR23:A735
Zentralblatt MATH: 0099.13502
Digital Object Identifier: doi:10.1214/aoms/1177705160
Project Euclid: euclid.aoms/1177705160
Kiefer, J. (1962). Two more criteria equivalent to D-optimality of designs. Ann. Math. Statist. 33 792-796.
Mathematical Reviews (MathSciNet): MR25:701
Zentralblatt MATH: 0116.11301
Digital Object Identifier: doi:10.1214/aoms/1177704597
Project Euclid: euclid.aoms/1177704597
Kiefer, J. (1974). General equivalence theory for optimal designs (approximate theory). Ann. Statist. 2 849-879.
Mathematical Reviews (MathSciNet): MR356386
Zentralblatt MATH: 0291.62093
Digital Object Identifier: doi:10.1214/aos/1176342810
Project Euclid: euclid.aos/1176342810
Kiefer, J. and Wolfowitz, J. (1959). Optimum designs in regression problems. Ann. Math. Statist. 30 271-294.
Mathematical Reviews (MathSciNet): MR21:3079
Digital Object Identifier: doi:10.1214/aoms/1177706252
Project Euclid: euclid.aoms/1177706252
Kiefer, J. and Wolfowitz, J. (1960). The equivalence of two extremum problems. Canad. J. Math. 12 363-366.
Mathematical Reviews (MathSciNet): MR22:8616
Kiefer, J. and Wolfowitz, J. (1964). Optimum extrapolation and interpolation designs. I. Ann. Inst. Statist. Math. 16 79-108.
Mathematical Reviews (MathSciNet): MR31:2806
Digital Object Identifier: doi:10.1007/BF02868577
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.
Mathematical Reviews (MathSciNet): MR2000g:01040
Digital Object Identifier: doi:10.1214/ss/1009212244
Project Euclid: euclid.ss/1009212244
Pazman, A. (1986). Foundations of Optimum Experimental Design. Riedel, Dordrecht.
Mathematical Reviews (MathSciNet): MR88d:62128
Zentralblatt MATH: 0588.62117
Pukelsheim, F. (1983). On optimality properties of simple block designs in the approximate design theory. J. Statist. Plann. Inference 8 193-208.
Mathematical Reviews (MathSciNet): MR85e:62149
Zentralblatt MATH: 0531.62070
Digital Object Identifier: doi:10.1016/0378-3758(83)90038-1
Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
Mathematical Reviews (MathSciNet): MR94k:62124
Pukelsheim, F. and Titterington, D. M. (1983). General differential and Lagrangian theory for optimal experimental design. Ann. Statist. 11 1060-1068.
Mathematical Reviews (MathSciNet): MR87j:62133
Zentralblatt MATH: 0592.62066
Project Euclid: euclid.aos/1176346321
Silvey, S. D. (1978). Optimal design measures with singular information matrices. Biometrika 65 553-559.
Mathematical Reviews (MathSciNet): MR80b:62092
Zentralblatt MATH: 0391.62054
Digital Object Identifier: doi:10.1093/biomet/65.3.553
JSTOR: links.jstor.org
Silvey, S. D. (1980). Optimal Design. Chapman and Hall, London.
Mathematical Reviews (MathSciNet): MR82d:62123
