Title: Misspecified covariance structure and optimal designs for prediction
Authors: Helmut Waldl - Johannes Kepler University Linz (Austria) [presenting]
Abstract: Modeling spatial or spatio-temporal data requires the choice of a (spatio)-temporal covariance function. Assumptions such as isotropy, stationarity or separability are usually used to make parameter estimation and prediction easier. Second-order stationarity, for instance, makes it possible to parametrize a covariance function with just a few parameters that may determine even high dimensional covariance matrices totally. In doing so, we will never use the correct covariance matrix for prediction. Especially when we are looking for good or optimal designs for prediction with respect to an arbitrary criterion, a misspecified covariance matrix may have severe impact on the quality of prediction of the seemingly optimal design. We compare the performance of different commonly used covariance structures for spatial models based on simulated data. Surprisingly even correlation functions enjoying the good reputation of being robust against model misspecification yield suboptimal prediction.