Optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors

Abstract

The problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed. The measurements are assumed to be corrupted by an unknown but bounded additive noise. The sampling design assumes that the number of samples is unconstrained and no replication is allowed. Two main results are shown: 1) for particular classes of linear models, the optimal number of measurements is equal to the number of parameters, as in the statistical context; 2) the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori, knowing only the model and the error structure.