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Title: K-optimal designs for parameters of shifted Ornstein-Uhlenbeck processes and sheets Authors:  Sandor Baran - University of Debrecen (Hungary) [presenting]
Abstract: Continuous random processes and fields are regularly applied to model temporal or spatial phenomena in many different fields of science, and model fitting is usually done with the help of data obtained by observing the given process at various time points or spatial locations. In these practical applications sampling designs which are optimal in some sense are of great importance. We investigate the properties of the K-optimal design for temporal and spatial linear regression models driven by Ornstein-Uhlenbeck processes and sheets, respectively, and highlight the differences compared with the classical D-optimal sampling. We study the problems of the existence of K-optimal designs and also investigate the dependence of the two designs on the covariance parameters of the driving processes. This information may be crucial for an experimenter in order to increase efficiency in practical situations. Finally, we present a simulation study displaying the superiority of the K-optimal design for large parameter values of the driving random process.