A Simple Solution for Optimal Chebyshev Regression Extrapolation

Abstract

A simplified solution is presented for the problem of finding a set of points and corresponding weights that will minimize the variance of the estimated value of a Chebyshev regression function at a point outside the interval of observations. This problem, among others, was solved by Kiefer and Wolfowitz [3] by means of game-theoretic methods. The solution here is based on a simple theorem in [2] and well known properties of Chebyshev systems of functions.