If an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations, Anderson showed that the following method is optimal. Starting with the highest (specified) degree the procedure is to test in sequence whether the coefficients are 0. In this paper optimal designs for Anderson's procedure are determined explicitly. The optimal design maximizes the minimum power of a given set of alternatives.
"Optimal Designs for Identifying the Degree of a Polynomial Regression." Ann. Statist. 23 (4) 1248 - 1266, August, 1995. https://doi.org/10.1214/aos/1176324708