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Treating bias as variance for experimental design purposes

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Abstract

When an empirical model is fitted to data, bias can arise from terms that have not been incorporated, and this can have an important effect on the choice of an experimental design. Here, the biases are treated as random, and the consequences of this action are explored for the fitting of models of first and second order.

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References

  • Bandemer, H., Näther, W. and Pilz, J. (1987). Once more: optimal experimental design for regression models (with discussion), Statistics, 18, 171–217.

    Google Scholar 

  • Box, G. E. P. and Draper, N. R. (1959). A basis for the selection of a response surface design, J. Amer. Statist. Assoc., 54, 622–654.

    Google Scholar 

  • Box, G. E. P. and Draper, N. R. (1963). The choice of a second order rotatable design, Biometrika, 50, 335–352.

    Google Scholar 

  • Bunke, H. and Bunke, O. (1986). Statistical Inference in Linear Models, Wiley, New York.

    Google Scholar 

  • Draper, N. R. and Guttman, I. (1986). Response surface designs in flexible regions, J. Amer. Statist. Assoc., 81, 1089–1094.

    Google Scholar 

  • Draper, N. R. and Lawrence, W. E. (1965a). Designs which minimize model inadequacies; cuboidal regions of interest, Biometrika, 52, 111–118.

    Google Scholar 

  • Draper, N. R. and Lawrence, W. E. (1965b). Mixtures designs for three factors, J. Roy. Statist. Soc. Ser. B, 27, 450–465.

    Google Scholar 

  • Draper, N. R. and Lawrence, W. E. (1966). The use of second-order “spherical” and “cuboidal” designs in the wrong regions, Biometrika, 53, 596–599.

    Google Scholar 

  • Draper, N. R. and Lawrence, W. E. (1967). Sequential designs for spherical weight functions, Technometrics, 9, 517–529.

    Google Scholar 

  • Kiefer, J. (1985). Collected Papers III, Design of Experiments, Springer, New York.

    Google Scholar 

  • Steinberg, D. M. (1985). Model robust response surface designs: scaling two-level factorials, Biometrika, 72, 513–526.

    Google Scholar 

  • Welch, W. J. (1983). A mean squared error criterion for the design of experiments, Biometrika, 70, 205–213.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Statistics Department, University of Wisconsin, 1210 West Dayton Street, 53706, Madison, WI, U.S.A.

    Norman R. Draper

  2. Statistics Department, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    Irwin Guttman

Authors
  1. Norman R. Draper
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  2. Irwin Guttman
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Draper, N.R., Guttman, I. Treating bias as variance for experimental design purposes. Ann Inst Stat Math 44, 659–671 (1992). https://doi.org/10.1007/BF00053396

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  • DOI: https://doi.org/10.1007/BF00053396

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