Some sufficient conditions for establishing (M, S)-optimality

Jacroux, Michael; Seely, Justus

doi:10.1016/0378-3758(80)90028-2

Cited by 12 publications

(2 citation statements)

References 2 publications

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“…Clearly an (M, S)-optimal non-binary design will belong to the class pK + Do. Further if Do is (M, S)-optimal then so is D (Jacroux and Seely, 1977). This prompts the following conjectures:…”

Section: Designs With K:» Vmentioning

confidence: 95%

Conjectures for Optimal Block Designs

John

Williams

1982

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary In the study and construction of optimal block designs over the past 20 years a number of conjectures have been repeatedly stated and used. The purpose of this note is to bring together some of these conjectures. Although known to those actively engaged in research in design, it is hoped that this note will stimulate other statisticians and mathematicians to give their attention to these unsolved problems.

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Section: Designs With K:» Vmentioning

confidence: 95%

Conjectures for Optimal Block Designs

John

Williams

1982

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…With regard to /9~(v, b, k) and /)~(v, b, k), it follows from the results of Jacroux and Seely [13] that…”

Section: Y~~2=a~+fl~+r2+e~~p Lmentioning

confidence: 92%

Some E and MV-optimal designs for the two-way elimination of heterogeneity

Jacroux

1985

Ann Inst Stat Math

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SummaryIt is well known that in experimental settings where v treatments are being tested in b blocks of size k, a group divisible design having parameters ~2=~1+1 and whose corresponding C-matrix has maximal trace is both E and MV-optimal among all possible competing designs. In this paper, we show that under certain conditions, the E and MVoptimal group divisible block designs mentioned in the previous sentence can be used to construct E and MV-optimal row-column designs to handle experimental situations in which heterogeneity is to be eliminated in two directions and where v treatments are being tested in b columns and k rows. Examples are given to illustrate how the results obtained can be applied.

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Nearly Balanced Designs

Cheng¹

2004

Encyclopedia of Statistical Sciences

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Some sufficient conditions for establishing (M, S)-optimality

Cited by 12 publications

References 2 publications

Conjectures for Optimal Block Designs

Conjectures for Optimal Block Designs

Some E and MV-optimal designs for the two-way elimination of heterogeneity

Nearly Balanced Designs

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