Identification of universally optimal circular designs for the interference model

Zheng, Wei; Ai, Mingyao; Li, Kang

doi:10.1214/16-aos1496

Cited by 11 publications

(30 citation statements)

References 35 publications

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“…Here, μ is the general mean, β i is the block effect, τ dði,jÞ is the direct effect of dði, jÞ, λ dði,jÀ1Þ is the neighbour effect of treatment dði, j À 1Þ from the left neighbour and ρ dði,jþ1Þ is that from the right neighbour, ε ij is the zero-mean error term and dði, jÞ denotes the treatment assigned to the jth plot of block i by the design d. Circular designs require dði,0Þ ¼ dði, kÞ and dði, k þ 1Þ ¼ dði,1Þ. There has been extensive research on circular designs estimating τ, such as Azaïs et al (1993), Druilhet (1999), Filipiak and Markiewicz (2012) and Zheng et al (2017). Here, we propose to remove the circular restriction and allow any treatment assignment on the guarding plots dði,0Þ and dði, k þ 1Þ.…”

Section: Problem Formulationmentioning

confidence: 99%

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Optimal non‐circular designs for interference models

Kong

Zheng

2023

Stat

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In many applications of block designs, the responses of plots are affected by treatments in neighbouring plots. What makes it more complicated is the border effect on the two edge plots caused by potential environmental impacts outside the blocks. For the latter, many researchers use two guarding plots next to the edge plots, for which we apply certain treatments to control these impacts. There have been extensive studies of designs under this set‐up; however, we observe that existing literature has been focusing on circular designs where the treatments applied to the border effects are the same as the edge plots on their opposite sides. This structural restriction is unnecessary in most applications. We consider non‐circular designs, where guarding plots are allowed to take any treatments by design. In this paper, optimal non‐circular designs are constructed for direct effects estimations. It is found that optimal non‐circular designs outperform optimal circular designs in many cases, especially for many commonly studied cases in the literature.

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Section: Problem Formulationmentioning

confidence: 99%

“…For ðk, t, nÞ ¼ ð5,5,5Þ and a more complex covariance matrix Σ 2 in (17). Zheng et al (2017) constructed the optimal CD copied as d CD in (17).…”

Section: Comparison Of Exact Designsmentioning

confidence: 99%

Optimal non‐circular designs for interference models

Kong

Zheng

2023

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“…Class B has been shown to produce (universally) optimal designs for various cases [2,5,8], since balanced designs use sequences from this class. Class A was shown by Zheng et al [13] to be important for non-trivial covariance matrices.…”

Section: P]mentioning

confidence: 99%

“…[2]. However, Zheng et al [13] showed that designs with sequences from class A can be efficient in some situations. Thus, we will consider the designs d A and d B that only consist of sequences from classes A or B, respectively, and calculate their efficiency.…”

Section: Observe Thatmentioning

confidence: 99%

On MSE-Optimal Circular Crossover Designs

Neumann

Kunert

2021

J Stat Theory Pract

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In crossover designs, each subject receives a series of treatments, one after the other in p consecutive periods. There is concern that the measurement of a subject at a given period might be influenced not only by the direct effect of the current treatment but also by a carryover effect of the treatment applied in the preceding period. Sometimes, the periods of a crossover design are arranged in a circular structure. Before the first period of the experiment itself, there is a run-in period, in which each subject receives the treatment it will receive again in the last period. No measurements are taken during the run-in period. We consider the estimate for direct effects of treatments which is not corrected for carryover effects. If there are carryover effects, this uncorrected estimate will be biased. In that situation, the quality of the estimate can be measured by the mean square error, the sum of the squared bias and the variance. We determine MSE-optimal designs, that is, designs for which the mean square error is as small as possible. Since the optimal design will in general depend on the size of the carryover effects, we also determine the efficiency of some designs compared to the locally optimal design. It turns out that circular neighbour-balanced designs are highly efficient.

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“…In avoiding systematic bias caused by these side effects, the interference model has gained its popularity in data analysis. Correspondingly, the optimal or efficient designs have been studied by Gill (1993), Druilhet (1999), Kunert and Martin (2000), Filipiak and Markiewicz (2003, 2005, Bailey and Druilhet (2004), Ai et al (2007), Ai et al (2009), Kunert and Mersmann (2011), Druilhet and Tinsson (2012) and Filipiak (2012), Li, Zheng and Ai (2015), Zheng (2015) and Zheng, Ai and Li (2017) among others. However, they all assumed the block to be in one-dimensional layout so that the side effects is only contributed by left and right neighbors.…”

Section: Introductionmentioning

confidence: 99%

Universally Optimal Designs for the Two-dimensional Interference Model

Hedayat,

Xu,

Zheng

2017

Preprint

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There have been some major advances in the theory of optimal designs for interference models. However, the majority of them focus on one-dimensional layout of the block and the study for two-dimensional interference model is quite limited partly due to technical difficulties. This paper tries to fill this gap. Specifically, it systematically characterizes all possible universally optimal designs simultaneously.Computational issues are also addressed with theoretical backup.

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Identification of universally optimal circular designs for the interference model

Cited by 11 publications

References 35 publications

Optimal non‐circular designs for interference models

Optimal non‐circular designs for interference models

On MSE-Optimal Circular Crossover Designs

Universally Optimal Designs for the Two-dimensional Interference Model

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