Optimizing the measurement processing order for linear regression

The problem of finding an optimal processing order for equi-spaced measurements taken for linear regression purposes is examined. Optimality is defined in the sense of producing the most statistically accurate estimates for the number of measurements already processed. The excellent performance of a locally optimal greedy strategy which produces non-inferior (Pareto) orderings in the context of multi-criterion optimization is evaluated from the viewpoint of optimal replicated experimental design theory. An accelerated version of the greedy algorithm and computationally efficient heuristic algorithms are presented.