Strong moderate deviation theorems

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

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    Abstract

    Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form $T(\alpha_n)$, where $T$ is a sublinear functional and $\alpha_n$ is the empirical process. The basic theorem is also applied on linear combinations of order statistics, leading to a substantial improvement of previous results.
    Original languageUndefined
    Pages (from-to)987-1003
    Number of pages17
    JournalAnnals of probability
    Volume20
    Issue number2
    DOIs
    Publication statusPublished - 1992

    Keywords

    • Cramer type large deviations
    • empirical process
    • strong approximation
    • sublinear functional
    • METIS-140514
    • linear combinations of order statistics
    • seminorm
    • Moderate deviations
    • IR-70374
    • goodness-of-fit tests

    Cite this

    Inglot, T., Kallenberg, W. C. M., & Ledwina, T. (1992). Strong moderate deviation theorems. Annals of probability, 20(2), 987-1003. https://doi.org/10.1214/aop/1176989814