Acknowledgements

We study robust sampling designs for model-based stratification, when the assumed distribution F0 (·) of an auxiliary variable x, and the variance function g0 (·) in the associated regression model, are only approximately specified. We first maximize the scaled prediction mean squared error (SPMSE) for the empirical best predictor over the neighbourhoods of F0 and g0. Then we obtain robust sampling designs which minimize this maximum SPMSE through a modified genetic algorithm with ‘artificial implantation’. The techniques are illustrated in two case studies of Australian sugar farms and MU281 population. i