Limiting values of large deviation probabilities of quadratic statistics

G.A.M. Jeurnink, W.C.M. Kallenberg

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    Abstract

    Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation probabilities of general quadratic statistics are obtained by relating them to large deviation probabilities of sums of k-dimensional random vectors. The results are applied, e.g., to generalized Cramér-von Mises statistics, including the Anderson-Darling statistic, Neyman's smooth tests, and likelihood ratio tests.
    Original languageEnglish
    Pages (from-to)168-185
    JournalJournal of multivariate analysis
    Volume35
    Issue number2
    DOIs
    Publication statusPublished - 1990

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    Keywords

    • Generalized Cramér-von Mises statistics
    • Likelihood ratio tests
    • Quadratic statistics
    • Exact Bahadur efficiency
    • Neyman's smooth tests
    • Large deviations
    • Eigenfunctions
    • Eigenvalues
    • Hilbert-Schmidt operator

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