On exact minimax wavelet designs obtained by simulated annealing

We construct minimax robust designs for estimating wavelet regression models. Such models arise from approximating an unknown nonparametric response by a wavelet expansion. The designs are robust against errors in such an approximation, and against heteroscedasticity. We aim for exact, rather than approximate, designs; this is facilitated by our use of simulated annealing. The relative simplicity of annealing allows for a much more complete treatment of some hitherto intractable problems initially addressed in Oyet and Wiens (J. Nonparametric Stat. 12 (2000) 837). Thus, we are able to exhibit integer-valued designs for estimating higher order wavelet approximations of nonparametric curves. The exact designs constructed for multiwavelet approximations of various orders are found to be symmetric and periodic, as anticipated in Oyet and Wiens (J. Nonparametric Stat. 12 (2000) 837). We also construct integer-valued designs based on the Daubechies wavelet system with a wavelet number of 5.