Discrete minimax designs for regression models with autocorrelated MA errors

Minimax robust designs for regression models with possible misspecification in the response and possible autocorrelated errors are investigated on discrete design spaces. The designs minimize the maximum value of the trace of the mean squared error (MSE) matrix, and the maximum is obtained over a class of departure functions from the regression response and a class of autocorrelated errors. In particular, classes of moving average error processes are studied. The maximum value of the trace of MSE is obtained analytically, and the minimax designs can be computed through an annealing algorithm. Several examples are given to show robust designs for polynomial regression.