Modifications and extensions of the method of virtual noise in correlated experimental design

Rok, strany: 2008, 125 - 133

We consider a random process (or field) $y( x) =η ( θ ,x) +ε ( x) $ defined on a set $\mathcal{X}$ and having a covariance function $C( x,z,β ) $ parametrized by $β $. The aim is to find an $N$-point design $\{x₁,…,x_N\} \subset \mathcal{X}$ without replications, and such that $θ $ and $β $ will be estimated (locally) optimally. For that purpose one can use the method of virtual noise, which consists of adding to each $y( x) $ for computational purposes a supplementary independent noise $ε_ξ ( x),$ which is a white noise with variances at each $x\in \mathcal{X}$ depending on a design measure $ξ $ We can approach the optimal design by iterative changes of $ξ $. We extend the method to the case that also $β$ is estimated, and we present alternative, simpler expressions for the variance of the virtual noise.

ISO 690:

Pázman, A., Laca, J. 2008. Modifications and extensions of the method of virtual noise in correlated experimental design. In Tatra Mountains Mathematical Publications, vol. 39, no.1, pp. 125-133. 1210-3195.

APA:

Pázman, A., Laca, J. (2008). Modifications and extensions of the method of virtual noise in correlated experimental design. Tatra Mountains Mathematical Publications, 39(1), 125-133. 1210-3195.