Vanishing shortcoming and asymptotic relative efficiency

Tadeusz Inglot, Wilbert C.M. Kallenberg, Teresa Ledwina

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    Abstract

    The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order efficiency, but in regular cases there is equivalence. The results are in particular applied on tests for goodness-of-fit.
    Original languageEnglish
    Pages (from-to)215-238
    Number of pages24
    JournalAnnals of statistics
    Volume2000
    Issue number28
    DOIs
    Publication statusPublished - 2000

    Keywords

    • Shortcoming
    • Pitman efficiency
    • intermediate or Kallenberg efficiency
    • MSC-62F05
    • MSC-62G10
    • MSC-62G20
    • EWI-12848
    • Bahadur efficiency
    • Anderson–Darling test
    • Cramér–von Mises test
    • IR-64800
    • METIS-140620

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  • Cite this

    Inglot, T., Kallenberg, W. C. M., & Ledwina, T. (2000). Vanishing shortcoming and asymptotic relative efficiency. Annals of statistics, 2000(28), 215-238. https://doi.org/10.1214/aos/1016120370