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.
Publié le : 1980-05-14
Classification:
Linear operator,
linear space,
mvlue,
optimum designs,
kernel Hilbert space,
62J05,
62K05,
62M99
@article{1176345015,
author = {Spruill, Carl},
title = {Optimal Designs for Second Order Processes with General Linear Means},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 652-663},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345015}
}
Spruill, Carl. Optimal Designs for Second Order Processes with General Linear Means. Ann. Statist., Tome 8 (1980) no. 1, pp. 652-663. http://gdmltest.u-ga.fr/item/1176345015/