Abstract
Let D(v,b,k) be a class of designs with ν treatments and b blocks, each of size k. We show that (i) if a variance-balanced design exists in D(v, b, k), then it is Ε-optimal. Let Δ(ν, b, k) ⊂ D(v, b, k) containing all the variance-balanced designs. Then we prove that (ii) a design d ∈′ Δ(ν, b,k) is ER-optimal in Δ(ν, b,k) if its replication numbers are as uniform as possible, (iii) a design d in Δ(ν, b,k) is AR-optimal and DR-optimal in Δ(ν, b, k) if its replication numbers are all equal except one, and (iv) a design d in Δ(ν, b, k) has maximum average efficiency in Δ(ν, b,k) if its replications numbers are all equal but one. Average efficiencies of designs in three classes are computed and tabulated at the end.
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Dedicated to Professor Narayanaswamy Balakrishnan on his sixtieth birthday.
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Mishra, N. Nonbinary variance-balanced designs-part I, optimality. J Stat Theory Pract 11, 63–75 (2017). https://doi.org/10.1080/15598608.2016.1258348
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DOI: https://doi.org/10.1080/15598608.2016.1258348
Keywords
- Proper block design
- connected design
- variance balance
- completely symmetric matrix
- C-matrix
- efficiency factors
- nonbinary designs