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最適行比較與列比較之行列設計 / Optimal row-column design for comparing row effects and column effects朱佩玲, Chu, Pei-Ling Unknown Date (has links)
在行列設計(row-column design)的架構下,當行總和與列總和皆為總試驗處理數的倍數時,我們考慮行效果與列效果的相互比較之最適性。延續Shah和Sinha(1993)的結果,在給定行總和及列總和的情況下,我們導出達成齊一最適設計(uniformly optimal design)的充分條件。此外,當總實驗單位固定時,達成全域最適設計(universally optimal design)的充分條件亦被求出。我們同時列舉許多相關的設計排列法。 / We consider the problem of comparing row effects and column effects in the row-column design setup when the row sizes and column sizes are all multiples of the number of treatments. Following the work of Shah and Sinha (1993), we derive a sufficient condition for uniformly optimal designs for given values of the row sizes and column sizes. We also derive a sufficient condition for universally optimal designs when the total number of experimental units is fixed. Several examples of designs with high efficiencies are provided.
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