OPTIMAL DESIGNS WITH RESPECT TO ELFVINGS PARTIAL MINIMAX CRITERION INPOLYNOMIAL REGRESSION

For the polynomial regression model on the interval [a, b] the optimal design problem with respect to Elfving's minimax criterion is conside red. It is shown that the minimax problem is related to the problem of determining optimal designs for the estimation of the individual para meters. Sufficient conditions are given guaranteeing that an optimal d esign for an individual parameter in the polynomial regression is also minimax optimal for a subset of the parameters. The results are appli ed to polynomial regression on symmetric intervals [-b, b] (b less-tha n-or-equal-to 1) and on nonnegative or nonpositive intervals where the conditions reduce to very simple inequalities, involving the degree o f the underlying regression and the index of the maximum of the absolu te coefficients of the Chebyshev polynomial of the first kind on the g iven interval. In the most cases the minimax optimal design can be fou nd explicitly.