Optimal designs for a growth curve model

Sober and Wild (Nonlinear Regression, Wiley, New York (1989) 343) considered the nonlinear fitting problem for a growth curve model E(Y\x) = beta(0) + beta(1)x + beta(2)x(alpha). In this paper, we will determine the D-, A- and E-optimal designs for this model, with,7, known, on the interval [a, b], a < b. If a greater than or equal to 0 and alpha > 1, then the D-, A- and E-optimal designs are supported on three points including the two end-points and one interior point of [a, b]. Moreover, the D-and E-optimal designs share the same support points. If b = - a = 1 and x = 2,3,..., then the D-, A- and E-optinial designs are symmetrically supported on four points including the two end-points. For the interval of the form [a, 1] (-1 less than or equal to a < 0), and alpha = 2,3,..., the optimal designs are supported on either three or four points. Moreover, the exact n-point D-optimal designs are shown numerically to be supported at the support of the approximate D-optimal designs if a greater than or equal to -1/2, alpha greater than or equal to 2 and n greater than or equal to 3. (C) 2002 Elsevier Science B.V. All rights reserved.