The precision of different experimental designs for a random field

Duby, Camille; Guyon, Xavier; Prum, Bernard

doi:10.1093/biomet/64.1.59

Cited by 22 publications

(8 citation statements)

References 3 publications

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“…The discrete planar expential process is the discrete version of the continuous planar exponential process (Duby et al (1977)) where the correlation between two points on the plane is decreasing exponentially with the distkce 8, p(s) = exp(-as), a = -lnX, thus giving Similarly we assume for square plots v = 1 and for nonsquare plots u = 4. This process will subsequently be denoted by E.…”

Section: Correlation Structuresmentioning

confidence: 99%

“…Two different correlation &uctures are considered, the doubly-geometric scheme (Martin (1979)) and the discrete planar exponential process, which may be considered as a discrete form of the correlation structure considered by Duby, Guyon and Prum (1977) which arises from sampling on a grid. These structures are introduced in the second section.…”

Section: Introductionmentioning

confidence: 99%

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On optimal experimental design under spatial correlation structures for square and nonsquare plot designs

Becher

1988

Communications in Statistics - Simulation and Computation

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Section: Correlation Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On optimal experimental design under spatial correlation structures for square and nonsquare plot designs

Becher

1988

Communications in Statistics - Simulation and Computation

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“…Some numerical comparisons using the continuous space correlation function p(s) = e-s are given by Duby et al (1977). Other comparisons can be made in a similar way.…”

Section: Er (Mres) = Er(mtr)mentioning

confidence: 99%

On the Design of Experiments Under Spatial Correlation

Martin

1986

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe implications for experimental design when the errors are spatially correlated are investigated. The first part of the paper considers the case when treatment effects are estimated by ordinary least-squares. If only treatment labels are randomized, then Aefficient designs are reasonably independent of the correlation structure, but this is not so for other efficiency criteria. If randomization of designs is considered within one of the classical design sets, then restricted randomizations may be chosen to reduce the variations in efficiency. The distributions of the usual sums of squares are also discussed. The second part considers the case when the analysis to be used is generalized least-squares using a known correlation matrix. Then for a particular correlation structure the efficiency orderings are relatively stable over different criteria, but there are important differences between long-range and short-range correlations whatever the criterion. The efficiency gain over ordinary least-squares is shown to be least for long-range structures. Predictions made from theoretical results on the torus (Martin, 1982) are shown to have some validity in the plane. In both parts numerical evaluations provide illustrations.

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“…After Whittle's work Matern was the first to use this approach; a section in Matern (1960) investigates the effect of plot size, whilst Matern (1970) uses the model for the comparison of experimental designs. There has been little use made of the technique since then, except for Pearce (1976), who investigated plot size, and Duby et al (1977) who made further comparisons of experimental designs. Since the original work of Whittle the model has been regarded as purely theoretical and no attempt has been made to fit it to observed data.…”

Section: Continuous Models Of Spatial Variationmentioning

confidence: 99%

“…The inclusion of such a term is practically important since it prevents the variance of total plot response from dropping to near zero at very small plot sizes. Duby et al (1977) include such a term in their model of field variation. However we will not be able to fit this term because, using data obtained from plots of uniform area, it cannot be distinguished from random variation related to area.…”

Section: Variation From Plantsmentioning

confidence: 99%

Continuous Second Order Models of Spatial Variation with Application to the Efficiency of Field Crop Experiments

Brewer

Mead

1986

Journal of the Royal Statistical Society. Series A (General)

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This paper develops the approach of using continuous second order models of spatial variation, as described by Matern (1970), for the purposes of comparing the efficiencies of alternative experimental designs and analyses for crop experiments. The development is in three stages. First, a form of model is derived which is capable of describing the most important features of variation of crop yield in the field. In the second stage, techniques for fitting the model to uniformity trial data are developed in such a way that all the important parameters of the model can be estimated and tested. Finally procedures are outlined for evaluating the expected residual mean square resulting from a given design and analysis on a field whose properties obey a given realization of the model. These procedures include classical design and analysis and neighbouring plot methods.

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The precision of different experimental designs for a random field

Cited by 22 publications

References 3 publications

On optimal experimental design under spatial correlation structures for square and nonsquare plot designs

On optimal experimental design under spatial correlation structures for square and nonsquare plot designs

On the Design of Experiments Under Spatial Correlation

Continuous Second Order Models of Spatial Variation with Application to the Efficiency of Field Crop Experiments

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