Design sensitivity, \(\widetilde {\varGamma }\) , governs the performance of a sensitivity analysis in the limit as the sample size increases, \(I \rightarrow \infty \) . In samples of moderate size, a sensitivity analysis may terminate at a Γ well below \(\widetilde {\varGamma }\) due to sampling variability. The Bahadur efficiency of a sensitivity analysis compares the performance of two statistics at a Γ below the minimum of their two design sensitivities. The Bahadur slope of a test statistic drops to zero as Γ increases to \(\widetilde {\varGamma }\) . The best statistic in a randomization test—a test at Γ = 1—is often different from the best statistic for larger Γ, and the Bahadur relative efficiency provides insight into performance at intermediate values of Γ.

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Efficiency of Sensitivity Analyses

  • Paul R. Rosenbaum

摘要

Design sensitivity, \(\widetilde {\varGamma }\) , governs the performance of a sensitivity analysis in the limit as the sample size increases, \(I \rightarrow \infty \) . In samples of moderate size, a sensitivity analysis may terminate at a Γ well below \(\widetilde {\varGamma }\) due to sampling variability. The Bahadur efficiency of a sensitivity analysis compares the performance of two statistics at a Γ below the minimum of their two design sensitivities. The Bahadur slope of a test statistic drops to zero as Γ increases to \(\widetilde {\varGamma }\) . The best statistic in a randomization test—a test at Γ = 1—is often different from the best statistic for larger Γ, and the Bahadur relative efficiency provides insight into performance at intermediate values of Γ.