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An asymptotics look at the generalized inference. (English) Zbl 1328.62184

Summary: This paper provides an asymptotics look at the generalized inference through showing connections between the generalized inference and two widely used asymptotic methods, the bootstrap and plug-in method. A generalized bootstrap method and a generalized plug-in method are introduced. The generalized bootstrap method can not only be used to prove asymptotic frequentist properties of existing generalized confidence regions through viewing fiducial generalized pivotal quantities as generalized bootstrap variables, but also yield new confidence regions for the situations where the generalized inference is unavailable. Some examples are presented to illustrate the method. In addition, the generalized \(F\)-test [S. Weerahandi, “ANOVA under unequal error variances”, Biometrics 51, No. 2, 589–599 (1995; doi:10.2307/2532947)] can be derived by the generalized plug-in method, then its asymptotic validity is obtained.

MSC:

62F25 Parametric tolerance and confidence regions
62F40 Bootstrap, jackknife and other resampling methods
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References:

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