On the normal approximations of V- and L-statistics

Yoshihiko Maesono

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    1 Citation (Scopus)

    Abstract

    The rates of convergence to the normal distribution are investigated for V- and L-statistics. We derive an inequality which gives a lower bound of the uniform distance between two distributions of the V-statistic and the normal distribution. We obtain an inequality which gives a lower bound of the uniform distance, and is meaningful in the case that the distribution of the standardized V-statistic is symmetric around the origin. Further, we also derive similar inequalities for the L-statistic. The proofs are based on Stein's method.

    Original languageEnglish
    Pages (from-to)291-314
    Number of pages24
    JournalJournal of Statistical Planning and Inference
    Volume42
    Issue number3
    DOIs
    Publication statusPublished - Dec 1994

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Statistics, Probability and Uncertainty
    • Applied Mathematics

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