On a Theorem of Hoel and Levine on Extrapolation Designs

J. Kiefer · Jacob Wolfowitz

53 citations0/0 files storedThe Annals of Mathematical Statistics

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Optimal Experimental Design Methods Mathematical functions and polynomials Advanced Statistical Methods and Models

Abstract

Recent results [5] of Hoel and Levine (1964), which assert that designs on $\lbrack -1, 1\rbrack$ which are optimum for certain polynomial regression extrapolation problems are supported by the "Chebyshev points," are extended to cover other nonpolynomial regression problems involving Chebyshev systems. In addition, the large class of linear parametric functions which are optimally estimated by designs supported by these Chebyshev points is characterized.

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1959Optimum Designs in Regression Problems 1992Optimum Experimental Designs 1953Locally Optimal Designs for Estimating Parameters 1952Optimum Allocation in Linear Regression Theory

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1969Recent Work on the Design of Experiments: A Bibliography and a Review 1972Optimal Designs for Estimating the Slope of a Polynomial Regression 1970Optimal Regression Designs with Previous Observations

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