Some aspects of experimental design and analysis when errors are correlated

Abstract

Generalized least squares estimation is considered for some designs on the torus when the errors are assumed to follow a known second-order stationary torus lattice process. Two general types of torus designs, regular and treatment-balanced, are presented. Ordinary least squares is shown to be optimal for regular designs, whilst certain treatment-balanced designs are shown to be optimum under a wide range of optimality criteria. The method of Papadakis is investigated, and shown to have simple solutions for these designs. The relation of a theoretical form of Papadakis's estimator to the generalized least squares estimator for the completely symmetric first-order conditional torus lattice process is considered.