On the normal approximations of V- and L-statistics

Yoshihiko Maesono

Research output: Contribution to journalArticle

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

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L-statistics
Normal Approximation
Statistics
Statistic
Gaussian distribution
Normal distribution
Lower bound
Stein's Method
Rate of Convergence
Approximation
Lower bounds

All Science Journal Classification (ASJC) codes

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

Cite this

On the normal approximations of V- and L-statistics. / Maesono, Yoshihiko.

In: Journal of Statistical Planning and Inference, Vol. 42, No. 3, 01.01.1994, p. 291-314.

Research output: Contribution to journalArticle

Maesono, Yoshihiko. / On the normal approximations of V- and L-statistics. In: Journal of Statistical Planning and Inference. 1994 ; Vol. 42, No. 3. pp. 291-314.
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