On Universal Optimality of Circular Weakly Neighbor Balanced Designs Under an Interference Model

Filipiak, Katarzyna; Markiewicz, Augustyn

doi:10.1080/03610926.2011.587932

Cited by 10 publications

(29 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For particular parameter sets, there exists a CWBD using fewer subjects than the circular balanced uniform designs whose universal optimality was proved by Magda (1980) and Kunert (1984b). The idea of the possible reduction of number of subjects follows from the universal optimality of circular weakly neighbour balanced designs under the interference model with left-neighbour effects, which is proved in Filipiak and Markiewicz (2012).…”

mentioning

confidence: 95%

“…Druilhet (1999), while for the existence of a CWBD the expression n(n − 2λ + 1) must be divisible by t − 1; cf. Filipiak and Markiewicz (2012). The design parameters satisfying the necessary condition for the existence of a CWBD with t ≤ 19 and n < 3(t − 1) are listed in Table 1 of Filipiak and Markiewicz (2012).…”

mentioning

confidence: 99%

“…Druilhet (1999) considered optimality of circular balanced designs (CBDs) for the estimation of direct as well as carry-over effects, while Bailey and Druilhet (2004) proved their optimality for the estimation of total effects. Filipiak and Markiewicz (2012) showed universal optimality of circular weakly balanced designs (CWBDs) for the estimation of direct effects only.…”

mentioning

confidence: 99%

“…Filipiak et al (2008) called the matrix S d the left-neighbouring matrix. When the number of treatments is equal to the number of periods, Filipiak and Markiewicz (2012) …”

mentioning

confidence: 99%

See 3 more Smart Citations

On Optimality and Construction of Circular Repeated-Measurements Designs

Bailey¹,

Cameron²,

Filipiak³

et al. 2017

STAT SINICA

Self Cite

View full text Add to dashboard Cite

mentioning

confidence: 95%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Filipiak et al (2008) called the matrix S d the left-neighbouring matrix. When the number of treatments is equal to the number of periods, Filipiak and Markiewicz (2012) …”

mentioning

confidence: 99%

See 2 more Smart Citations

On Optimality and Construction of Circular Repeated-Measurements Designs

Bailey¹,

Cameron²,

Filipiak³

et al. 2017

STAT SINICA

Self Cite

View full text Add to dashboard Cite

“…From Filipiak and Markiewicz (2012) it follows that a necessary condition for the existence of a CWNBD with…”

Section: Possible Extensions For Specific Vmentioning

confidence: 99%

Universally optimal designs under mixed interference models with and without block effects

Filipiak

Markiewicz

2017

Metrika

Self Cite

View full text Add to dashboard Cite

The literature on neighbor designs as introduced by Rees (Biometrics 23:779-791, 1967) is mainly devoted to construction methods, providing few results on their statistical properties, such as efficiency and optimality. A review of the available literature, with special emphasis on the optimality of neighbor designs under various fixed effects interference models, is given in Filipiak and Markiewicz (Commun Stat Theory Methods 46:1127-1143, 2017). The aim of this paper is to verify whether the designs presented by Filipiak and Markiewicz (2017) as universally optimal under fixed interference models are still universally optimal under models with random interference effects. Moreover, it is shown that for a specified covariance matrix of random interference effects, a universally optimal design under mixed interference models with block effects is universally optimal over a wider class of designs. In this paper the method presented by Filipiak and Markiewicz (Metrika 65:369-386, 2007) is extended and then applied to mixed interference models without or with block effects.

show abstract

Optimal non‐circular designs for interference models

Kong

Zheng

2023

Stat

View full text Add to dashboard Cite

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.

show abstract

On Universal Optimality of Circular Weakly Neighbor Balanced Designs Under an Interference Model

Cited by 10 publications

References 12 publications

On Optimality and Construction of Circular Repeated-Measurements Designs

On Optimality and Construction of Circular Repeated-Measurements Designs

Universally optimal designs under mixed interference models with and without block effects

Optimal non‐circular designs for interference models

Contact Info

Product

Resources

About