Optimal designs for linear models with Fredholm-type errors

Abstract A new class of estimators, matrix weighted estimators (MWEs), have been proposed for the parameters in linear models with correlated errors. In this paper, we consider the design problem for linear models with Fredholm-type errors, i.e., the errors with continuous covariance kernels, when MWEs are used. By applying the tools of stochastic analysis and measure theory, we derive the analytical expressions of the optimal designs under some restrictions. To treat the general cases, an approximation method for the optimal designs is then introduced, which can reduce the computational cost. Practical implementations for obtaining designs with finite sample sizes are demonstrated. Numerical examples show that the obtained approximate designs are very close to the optimal ones.