The Annals of Statistics

Optimal Designs for Second Order Processes with General Linear Means

Carl Spruill

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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


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