Optimal designs for Gaussian random field regression models

The present paper deals with optimal designs for random field regression models in the univariate case. In particular we consider the problem of designing experiments (i.e. sampling in time or in the real line) when the observations can be modelled via a Gaussian process with a regressive trend component and an exponential correlation structure. This modelling approach has been widely used for the analysis of computer experiments (see for instance Sacks, Welch, Mitchell and Wynn, 1989) and in empirical and theoretical finance, in order to model continuous time interest rates (see Gourieroux and Jasiak, 2008). Assuming the Maximum Likelihood approach, we study the optimal design problem for the estimation of the unknown parameters of the model using a criterion based on the Fisher information matrix. Sacks J., Welch W.J., Mitchell T.J. and Wynn H.P. (1989) Design and analysis of computer experiments, Statistical Sciences, 4, 409-423. Gourieroux C. and Jasiak J. (2008) Financial Econometrics: Problems, Models, and Methods. Princeton University Pres