A frequency domain comparison of estimation methods for Gaussian fields

This paper demonstrates that well-known parameter estimation methods for Gaussian fields place different emphasis on the high and low frequency components of the data. As a consequence, the relative importance of the frequencies under the objective of the analysis should be taken into account when selecting an estimation method, in addition to other considerations such as statistical and computational efficiency. The paper also shows that when noise is added to the Gaussian field, maximum pseudolikelihood automatically sets the smoothing parameter of the model equal to one. A simulation study then indicates that generalised cross-validation is more robust than maximum likelihood under model misspecification in smoothing and image restoration problems. This has implications for Bayesian procedures since these use the same weightings of the frequencies as the likelihood.