On Local and Nonlocal Measures of Efficiency

Wilbert C.M. Kallenberg, Teresa Ledwina

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    General results on the limiting equivalence of local and nonlocal measures of efficiency are obtained. Why equivalence occurs in so many testing and estimation problems is clarified. Uniformity of the convergence is a key point. The concepts of Frechet- and Hadamard-type differentiability, which imply uniformity, play an important role. The theory is applied to tests based on linear rank statistics, showing equivalence of the local limit of exact Bahadur efficiency and Pitman efficiency. As a second application, the relation between the inaccuracy rate and the asymptotic variance of $L$-estimators is investigated.
    Original languageEnglish
    Pages (from-to)1401-1420
    JournalAnnals of statistics
    Issue number4
    Publication statusPublished - 1987


    • IR-70376
    • $L$-estimators
    • inaccuracy rate
    • Exact Bahadur efficiency
    • linear rank statistics
    • Hadamard-type differentiability
    • Pitman efficiency
    • Large deviations
    • Frechet-type differentiability
    • Asymptotic variance

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