Conditions for the robustness of block designs against the unavailability of data. (English) Zbl 0646.62068
Summary: According to the concept of S. Ghosh, ibid. 6, 25-32 (1982; Zbl 0473.62060), a binary and connected block design D, with the smallest treatment replication \(r_{[v]}\), is said to be maximally robust against the unavailability of data and with respect to the estimability of treatment contrasts, if a design \(D_{\#}\), obtained from D by deleting any \(r_{[v]}-1\) blocks, remains connected irrespective of the choice of the blocks deleted. Three sufficient conditions for maximal robustness of a block design are derived. Their applications are shown in the context of certain variance-balanced block designs constructed by S. Kageyama, Utilitas Math. 9, 209-229 (1976; Zbl 0334.05013), and variance-and-efficiency-balanced block designs listed by S. C. Gupta and B. Jones, Biometrika 70, 433-440 (1983; Zbl 0521.62062).
Keywords:
BIB design; connectedness; smallest treatment replication; unavailability of data; estimability of treatment contrasts; sufficient conditions for maximal robustness; variance-balanced block designs; efficiency-balanced block designsReferences:
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