Designs for varietal experiments in the presence of trends

Lin, Win-Chin

doi:10.31274/rtd-180813-10792

Cited by 1 publication

(2 citation statements)

References 36 publications

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“…If, in addition, σ 2 θ = 0, then the model is equivalent to one in which the trend is fixed, linear and the same for each block. This has been studied by several authors, including Bradley and Yeh [1], Yeh and Bradley [21], Yeh, Bradley and Notz [22], Stufken [20], Lin and Dean [11], Chai and Majumdar [3], Chai [2] and Lin and Stufken [12,13]. Alternatively, if σ 2 θ = ∞, then the model is still equivalent to one in which the trend is fixed and linear, but now possibly different in different blocks.…”

Section: Setup and Basic Resultsmentioning

confidence: 99%

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Optimal designs for mixed models in experiments based on ordered units

Majumdar

Stufken

2008

Ann. Statist.

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We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.Comment: Published in at http://dx.doi.org/10.1214/07-AOS518 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Setup and Basic Resultsmentioning

confidence: 99%

“…For some examples and further discussion and references, we refer the reader to Bradley and Yeh [1], Chai and Majumdar [3], Lin and Dean [11], Lin and Stufken [12], Jacroux, Majumdar and Shah [7,8] and Majumdar and Martin [15]. Lin and Stufken [12] also contains some additional discussion on the pros and cons of using systematic designs.…”

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confidence: 99%

Optimal designs for mixed models in experiments based on ordered units

Majumdar

Stufken

2008

Ann. Statist.

View full text Add to dashboard Cite

show abstract

Designs for varietal experiments in the presence of trends

Cited by 1 publication

References 36 publications

Optimal designs for mixed models in experiments based on ordered units

Optimal designs for mixed models in experiments based on ordered units

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