Robust sampling designs for a possibly misspecified stochastic process

We address the problem of finding robust sampling designs for the estimation of a discrete time second-order stationary process when its autocorrelation function is only approximately specified and has a spectral density belonging to a neighbourhood of a specified ‘base’ density. The value of the stochastic process is predicted by the best – for the assumed autocorrelation function – linear unbiased predictor on the basis of a finite sample of observations. Following the approach of minimax robustness, we find the least favourable – in the sense of maximizing the average mean squared error (amspe) of these predictions – spectral density. We then obtain, through a genetic algorithm, robust sampling designs which minimize this maximum amspe. Several examples are discussed and assessed, on the basis of which we conclude that the robust designs can offer substantial protection against model errors, at a minimal cost in efficiency at the base model. The techniques are illustrated in a case study, using a series of interest in statistical climatology.