Robustness in spatial studies II: minimax design

Wiens, Douglas P.

doi:10.1002/env.701

Cited by 14 publications

(13 citation statements)

References 16 publications

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“…Quite often in practice the same data set is used for both parameter estimation and spatial prediction; thus, it is important to have designs that are good for prediction with estimated parameters. Caselton et al (1992), Banjevic and Switzer (2002), Wiens (2005), Zimmerman (2005), and Zhu and Stein (2005b) have considered different aspect of this problem in recent years. Due to the spatial correlation that usually exists among the spatial sites, optimal designs for both estimation and prediction are very difficult to be given explicitly.…”

Section: Introductionmentioning

confidence: 97%

Spatial sampling design under the infill asymptotic framework

Zhu

Zhang

2006

Environmetrics

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SUMMARYWe study optimal sample designs for prediction with estimated parameters. Recent advances in the infill asymptotic theory provide a deeper understanding of the finite sample behavior of prediction and estimation. By incorporating these known asymptotic results, we modify some existing design criteria for estimation of covariance function and best linear unbiased prediction. These modified criteria could significantly reduce the computation time necessary for finding an optimal design. We illustrate our approach through both a real experiment in agriculture and simulation.

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Section: Introductionmentioning

confidence: 97%

Spatial sampling design under the infill asymptotic framework

Zhu

Zhang

2006

Environmetrics

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“…Wiens [107] discusses robust designs for spatial processes in the face of uncertainty about measurement errors and the spatial covariance. A minimax approach is adopted.…”

Section: Model-based Designmentioning

confidence: 99%

Sparse sampling: Spatial design for monitoring stream networks

Dobbie¹,

Henderson²,

Stevens³

2008

Statist. Surv.

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Spatial designs for monitoring stream networks, especially ephemeral systems, are typically non-standard, `sparse' and can be very complex, reflecting the complexity of the ecosystem being monitored, the scale of the population, and the competing multiple monitoring objectives. The main purpose of this paper is to present a review of approaches to spatial design to enable informed decisions to be made about developing practical and optimal spatial designs for future monitoring of streams.Comment: Published in at http://dx.doi.org/10.1214/07-SS032 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…Wiens () obtained a robust predictor of Y ( t ) in the face of uncertainty (U1). Furthermore, Wiens () considered designs robust against misspecified models. Wiens & Zhou () proposed methods to construct robust designs for a test‐control field experiment with particular attention paid to the effects of both (U1) and (U2).…”

Section: Introductionmentioning

confidence: 99%

Robust design for the estimation of a threshold probability

2018

Can J Statistics

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We consider the construction of robust sampling designs for the estimation of threshold probabilities in spatial studies. A threshold probability is a probability that the value of a stochastic process at a particular location exceeds a given threshold. We propose designs such that the estimation of threshold probabilities is robust to two possible model uncertainties: misspecified regression responses and covariance structures. To address these two uncertainties of this stochastic process, we average the mean squared error of the predicted values relative to the true values, over all possible covariance structures in a neighbourhood of the experimenter's nominal choice, and then maximize it over a neighbourhood of the fitted model. Finally, the maximum is minimized to obtain the robust designs. The Canadian Journal of Statistics 46: 470–481; 2018 © 2018 Statistical Society of Canada

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Robustness in spatial studies II: minimax design

Cited by 14 publications

References 16 publications

Spatial sampling design under the infill asymptotic framework

Spatial sampling design under the infill asymptotic framework

Sparse sampling: Spatial design for monitoring stream networks

Robust design for the estimation of a threshold probability

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