Optimal Designs for Second Order Processes with General Linear Means

Abstract

For each $x$ in some factor space $X$ an experiment can be performed whose outcome is $\{Y(x, t): t \in T \rbrack$ where $Y(x, t) = m_x(\theta, t) + \varepsilon(t)$. The zero mean error process $\varepsilon(t)$ has known covariance function $K$ and the maps $m_x$ (of known form) are linear from the parameter space $\Theta$ to the rkhs generated by $K$. Expressions for the variance of the umvlue of $\tau(\theta)$ (where $\tau$ is linear) are given which are analogous to the formulas in the finite dimensional $\Theta$ case. An Elfving's theorem is proved and a number of examples are given.