Estimation under invariant distributions

Hajime Yamato, Yoshihiko Maesono

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


If a distribution is invariant under a finite group of transformations, an estimator of a parameter associated with the distribution is improved by making it invariant. The resulting invariant estimator is characterized as the projection of the original estimator. If the estimator is the uniformly minimum variance unbiased estimator of its expectation for continuous distributions, then the invariant estimator is the uniformly minimum variance unbiased estimator for invariant and continuous distributions. A typical example is U-statistics and invariant U-statistics.

Original languageEnglish
Pages (from-to)55-61
Number of pages7
JournalJournal of Statistical Planning and Inference
Issue number1
Publication statusPublished - May 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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