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Optimal experimental design

Advanced Review

Valerii Fedorov

Published Online: Sep 08 2010

DOI: 10.1002/wics.100

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Abstract After a short historical introduction, the properties and numerical methods are the focal point of discussion. Construction of discrete and adaptive designs demand more extended exposition and are beyond the scope of this article but the information about the corresponding publications is provided. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical Models > Linear Models Statistical Models > Classification Models

References

Smith, K. On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika 1918, 12: 1–85.
Wald, A. On the efficient design of statistical investigations. Ann Math Stat 1943, 14: 134–140.
Elfving, G. Optimum allocation in linear regression theory. Ann Math Stat 1952, 23: 255–262.
Silvey, SD, Titterington, DM. A geometric approach to optimal design theory. Biometrika 1973, 60: 15–19.
Guest, PG. The spacing of observations in polynomial regression. Ann Math Stat 1958, 29: 294–299.
Hoel, PG. Efficiency problems in polynomial estimation. Ann Math Stat 1958, 29: 1134–1145.
Kiefer, J, Wolfowitz, J. Optimum design in regression problem. Ann Math Stat 1959, 30: 271–294.
Kiefer, J, Wolfowitz, J. The equivalence of two extremum problems. Can J Math 1960, 12: 363–366.
Karlin, S, Studden, W. Tchebysheff Systems: With Applications in Analysis and Statistics. New York: John Wiley %26 Sons; 1966.
Fedorov, V. The design of experiments in multiresponse case. Theory Probab Appl 1971, 16: 323–332.
Fedorov, V. Theory of Optimal Experiments. New York: Academic Press; 1972.
Chernoff, H. Locally optimal designs for estimating parameters. Ann Math Stat 1953, 24: 586–602.
Chernoff, H. Sequential Analysis and Optimal Design. Philadelphia, PA: SIAM; 1972.
Box, GEP, Lucas, HL. Design of experiments in nonlinear situations. Biometrika 1959, 46: 77–90.
Box, GEP, Hunter, WG. Sequential design of experiments for nonlinear models. In: Korth, JJ, ed. Proceedings IBM Scientific Computing Symposium: Statistics. White Plains: IBM; 1965, 113–137.
Lindley, DV. On measure of information provided by an experiment. Ann Math Stat 1956, 27: 986–1005.
Fedorov, VV, Pázman, A. Design of physical experiments (statistical methods). Fortschr Phys 1968, 24: 325–345.
Caselton, WF, Zidek, JV. Optimal monitoring network designs. Stat Probab Lett 1984, 2: 223–227.
Caselton, WF, Kan, L, Zidek, JV. Quality data networks that minimize entropy. In: Walden, AT, Guttorp, P, eds. Statistics in the Environmental and Earth Sciences. London: Arnold; 1992, 10–38.
Sebastiani, P, Wynn, HP. Maximum entropy sampling and optimal Bayesian experimental design. J R Stat Soc B 2000, 62: 145–157.
Ermakov, SM, ed. Mathematical Theory of Experimental Design [in Russian]. Moscow: Nauka; 1983.
Pilz, J. Bayesian Estimation and Experimental Design in Linear Regression Models. New York: John Wiley %26 Sons; 1991.
Chaloner, K, Verdinelli, I. Bayesian experimental design: a review. Stat Sci 1995, 10: 273–304.
Wynn, HP. The sequential generation of D‐optimal experimental designs. Ann Math Stat 1970, 14: 134–140.
Fedorov, VV, Malyutov, MB. Optimal designs in regression problems. Math Oper Stat 1972, 3: 281–308.
Atwood, CL. Sequences converging to D‐optimal design of experiments. Ann Stat 1973, 1: 342–352.
Fedorov, VV, Uspensky, AB. Numerical Aspects of Design and Analysis of Experiments. Moscow: Moscow State University Press; 1975.
Mitchell, TJ. An algorithm for construction of D‐optimal experimental designs. Technometrics 1974, 16: 203–211.
Silvey, SD. Optimal Design. London: Chapman and Hall; 1980.
Nachtsheim, CJ. Tools for computer‐aided design of experiments. J Qual Technol 1987, 19: 132–160.
Atkinson, AC, Donev, AN. Optimum Experimental Designs. Oxford: Oxford University Press; 1992.
Gaffke, N, Mathar, R. On a class of algorithms from experimental design theory. Optimization 1992, 24: 91–126.
Fedorov, VV, Hackl, P. Model‐oriented Design of Experiments. New York: Springer; 1997.
Atkinson, AC, Donev, AN, Tobias, RD. Optimum Experimental Design, with SAS. Oxford: Oxford University Press; 2007.
Pukelsheim, F. Optimal Design of Experiments. New York: John Wiley %26 Sons; 1993.
Cook, RD, Fedorov, VV. Constrained Optimization of Experimental design (with Discussion). Statistics 1995, 26: 129–178.
Atkinson, AC, Cox, DR. Planning experiments for discriminating between models (with discussion). J R Stat Soc [Ser A] 1974, 36: 321–348.
Läuter, E. Experimental design in a class of models. Math Oper Stat Ser Stat 1974, 5: 379–398.
Atkinson, AC, Fedorov, VV. The design of experiments for discriminating between two rival models. Biometrika 1975, 62: 57–70.
Atkinson, AC, Fedorov, VV. Optimal design: experiments for discriminating between several models. Biometrika 1975, 62: 289–303.
Fedorov, V, Khabarov, V. Duality of optimal designs for model discrimination and parameter estimation. Biometrika 1986, 73: 183–190.
Box, GEP, Hill, WJ. Discrimination among mechanistic models. Technometrics 1967, 9: 57–71.
Sacks, J, Ylvisaker, D. Designs for regression problems with correlated errors. Ann Math Stat 1966, 37: 66–89.
Sacks, J, Ylvisaker, D. Designs for regression problems with correlated errors, many parameters. Ann Math Stat 1968, 39: 49–69.
Sacks, J, Ylvisaker, D. Designs for regression problems with correlated errors, III. Ann Math Stat 1970, 39: 2057–2074.
Cambanis, S. Sampling designs for time series. Handbook of Statistics, vol. 5. New York: North‐Holland; 1985, 337–362.
Matern, B. Spatial Variation. Berlin: Springer‐Verlag; 1986.
Der Megreditchian, G. L’optimization des réseaux d`observation des champs météorologiques. Météorologie 1979, 6: 51–66.
Micchelli, CA, Wahba, G. Design problem for optimal surface interpolation. In: Ziegler, Z, ed. Approximation Theory and Applications. New York: Academic Press; 1981, 329–348.
Fedorov, VV. Design of spatial experiments: model fitting and prediction. In: Ghosh, S, Rao, CR, eds. Handbook of Statistics, vol. 13. New York: Elsevier Science; 1996, 515–553.
Guttorp, P, Le, ND, Sampson, PD, Zidek, JV. Using entropy to redisign of environmental monitoring network. In: Patil, GP, Rao, CR, eds. Multivariate Environmental Statistics. New York: Elsevier Science; 1993, 175–202.
Martin, RJ. Spatial experimental design. In: Ghosh, S, Rao, CR, eds. Handbook of Statistics, Vol. 13. New York: Elsevier Science; 1996, 477–514.
Wu, CEJ, Hamada, M. Experiments: Planning, Analysis and Parameter Design Optimization. New York: John Wiley %26 Sons; 2000.
Colbourn, C, Dinitz, J, eds. Handbook on Combinatorial Designs. New York: CRC; 2007.
Hu, F, Rosenberger, W. The Theory of Response‐Adaptive Randomization in Clinical Trials. New York: John Wiley %26 Sons; 2006.
Kiefer, J. Optimum experimental design. JRSS 1959, 21: 272–303.
Vandenberghe, L, Boyd, S. Semidefinite programming. SIAM Rev 1996, 38: 49–95.
Hiriart‐Urruty, J‐P, Lemaréchal, C. Convex Analysis and Minimization Algorithms I. New York: Springer; 1993.
Dragalin, V, Fedorov, V, Wu, Y. Adaptive designs for selecting drug combinations based on efficacy–toxicity response. J Stat Plan Inference 2008, 138: 352–373.
Harville, DA. Matrix Algebra from a Statistician`s Perspective. New York: Springer; 1997.
Whittle, P. Some General Points in the Theory of Optimal Experimental Design. J R Stat Soc Ser B 1973, 35: 123–130.
Lee, CM‐S. Constrained optimal designs. JSPI 1988, 18: 377–389.
Wynn, HP. Optimum submeasures with applications to finite population sampling. Statistical Decision Theory and Related Topics III, vol. 2. New York: Academic Press; 1982, 485–495.
Fedorov, V. Optimum design of experiments with bounded density: optimization algorithms of exchange type. J Stat Plan Inference 1989, 24: 1–13.
Cook, RD, Thibodeau, LA. Marginally restricted D–optimal designs. JASA 1980, 75: 366–371.
Fedorov, VV, Nachtsheim, C. Optimal design for time‐dependent responces. In: Kitsos, C, Müller, W, eds. MODA4–Advances in Model‐Oriented Data Analysis. New York: Springer; 1995.
Huang, ML, Hsu, MC. Marginally restricted linear–optimal designs. JSPI 1993, 35: 251–266.
Schwabe, R. Optimum Designs for Multi‐factor Models. New York: Springer; 1996.
Gaffke, N, Heiligers, B. On a class of algorithms from experimental design theory. Optimization 1992, 24: 91–126.
Gaffke, N, Heiligers, B. Algorithms for optimal design with application to multiple polynomial regression. Metrika 1995, 42: 173–190.
Gaffke, N, Heiligers, B. Second order methods for solving extremum problems from optimal linear regression design. Optimization 1995, 36: 41–57.
Cook, RD, Nachtsheim, CJ. Computer–aided blocking for factorial and response–surface designs. Technometrics 1989, 31: 339–346.
Gaivoronski, A. Linearization methods for optimization of functionals which depend on probability measures. Math Program Study 1986, 28: 157–181.

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