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 - Jan 1 1994

All Science Journal Classification (ASJC) codes

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

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