On a Theorem of Hoel and Levine on Extrapolation Designs

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.