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Optimum extrapolation and interpolation designs, I

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Summary

For regression problems where observations may be taken at points in a set X which does not coincide with the set Y on which the regression function is of interest, we consider the problem of finding a design (allocation of observations) which minimizes the maximum over Y of the variance function (of estimated regression). Specific examples are calculated for one-dimensional polynomial regression when Y is much smaller than or much larger than X. A related problem of optimum estimation of two regression coefficients is studied. This paper contains proofs of results first announced at the 1962 Minneapolis Meeting of the Institute of Mathematical Statistics. No prior knowledge of design theory is needed to read this paper.

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Authors and Affiliations

  1. Cornell University, USA

    J. Klefer & J. Wolfowitz

Authors
  1. J. Klefer
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  2. J. Wolfowitz
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Additional information

John Simon Guggenheim Memorial Foundation Fellow. Research supported in part by the office of Naval Research under Contract No. Nonr 266(04) (NR 047-005).

The research of this author was supported in part by the U.S. Air Force under Contract No. AF 18(600)-685.

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Klefer, J., Wolfowitz, J. Optimum extrapolation and interpolation designs, I. Ann Inst Stat Math 16, 79–108 (1964). https://doi.org/10.1007/BF02868564

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  • DOI: https://doi.org/10.1007/BF02868564

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