DISCRIMINATION DESIGNS FOR POLYNOMIAL, REGRESSION ON COMPACT INTERVALS

In the polynomial regression model of degree m is an element of N we c onsider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new opti mality criterion which minimizes a weighted p-mean of the variances of the least squares estimators for the coefficients of x(l) in the poly nomial regression models of degree l = 1,..., m. The theory of canonic al moments is used to determine the optimal designs with respect to th e proposed criterion. It is shown that the canonical moments of the op timal measure satisfy a (nonlinear) equation and that the support poin ts are given by the zeros of an orthogonal polynomial. An explicit sol ution is given for the discrimination problem between polynomial regre ssion models of degree m - 2, m - 1 and m and the results are used to calculate the discrimination designs in the sense of Atkinson and Cox for polynomial regression models of degree 1,..., m.