A general approach to optimal control of a regression experiment

Let = (1, 2, ..., n)' be the least-squares estimator of [theta] = ([theta]1, [theta]2, ..., [theta]n)' by the realization of the process y(t) = [Sigma]k = 1n [theta]kfk(t) + [xi](t) on the interval T = [a, b] with f = (f1, f2, ..., fn)' belonging to a certain set X. The process satisfies E([xi](t))[reverse not equivalent]0 and has known continuous covariance r(s, t) = E([xi](s)[xi](t)) on T - T. In this paper, A-, D-, and Ds-optimality are used as criteria for choosing f in X. A-, D-, and Ds-optimal models can be constructed explicitly by means of r.