Annals of the Institute of Statistical Mathematics

, Volume 16, Issue 1, pp 79–108

# Optimum extrapolation and interpolation designs, I

• J. Klefer
• J. Wolfowitz
Article

## 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.

## Keywords

Payoff Polynomial Interpolation Interpolation Problem Symmetric Design Chebyshev Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
N. I. Achieser,Theory of Approximation, Ungar Pub. Co., New York, 1956.
2. [2]
W. Behnken and G. E. P. Box, “Simplex sum designs,”Ann. Math. Stat., 31 (1960), 838–864.
3. [3]
A. Erdelyi (editor),Higher Transcendental Functions, 2, McGraw-Hill, New York, 1953.
4. [4]
L. B. W. Jolley,Summation of Series, Dover, New York, 1961.
5. [5]
J. Kiefer, “Optimum experimental designs,”J. Roy. Stat. Soc. (B), 21 (1959), 273–319.
6. [6]
J. Kiefer, “Optimum experimental designs V,”Proc. 4th Berkeley Symp., I (1960), 381–405.Google Scholar
7. [7]
J. Kiefer, “Optimum designs in regression problems II,”Ann. Math. Stat., 32 (1961), 298–325.
8. [8]
J. Kiefer, “An extremum result,”Can. J. Math., 14 (1962), 597–601.
9. [9]
J. Kiefer, “Two more criteria equivalent to D-optimality of designs,“Ann. Math. Stat., 33 (1962), 792–796.
10. [10]
J. Kiefer and J. Wolfowitz, “Optimum designs in regression problems,”Ann. Math. Stat., 30 (1959), 271–294.
11. [11]
J. Kiefer and J. Wolfowitz, “The equivalence of two extremum problems,”Can.J. Math., 12 (1960), 363–366.
12. [12]
P. G. Hoel and A. Levine, “ Optimal spacing and weighting in polynomial prediction,” to appear in Ann, Math, Stat.Google Scholar

© Institute of Statistical Mathematics 1964

## Authors and Affiliations

• J. Klefer
• 1
• J. Wolfowitz
• 1
1. 1.Cornell UniversityUSA