## The Annals of Statistics

- Ann. Statist.
- Volume 8, Number 3 (1980), 652-663.

### 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.

#### Article information

**Source**

Ann. Statist., Volume 8, Number 3 (1980), 652-663.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345015

**Digital Object Identifier**

doi:10.1214/aos/1176345015

**Mathematical Reviews number (MathSciNet)**

MR568727

**Zentralblatt MATH identifier**

0486.62071

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62J05: Linear regression

Secondary: 62K05: Optimal designs 62M99: None of the above, but in this section

**Keywords**

Linear operator linear space mvlue optimum designs kernel Hilbert space

#### Citation

Spruill, Carl. Optimal Designs for Second Order Processes with General Linear Means. Ann. Statist. 8 (1980), no. 3, 652--663. doi:10.1214/aos/1176345015. https://projecteuclid.org/euclid.aos/1176345015