Sample quantiles and additive statistics: Information, sufficiency, estimation

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The order of the increase in the Fisher information measure contained in a finite number k of additive statistics or sample quantiles, constructed from a sample of size n, as n → ∞, is investigated. It is shown that the Fisher information in additive statistics increases asymptotically in a manner linear with respect to n, if 2 + δ moments of additive statistics exist for some δ > 0. If this condition does not hold, the order of increase in this information is non-linear and the information may even decrease. The problem of asymptotic sufficiency of sample quantiles is investigated and some linear analogues of maximum likelihood equations are constructed. AMS classifications: Primary 62B10, 62E20, 62F10, 62F12.

Original languageEnglish
Pages (from-to)93-108
Number of pages16
JournalJournal of Statistical Planning and Inference
Issue number1
StatePublished - 1 Jun 1996


  • Additive statistics
  • Asymptotic sufficiency
  • Estimation
  • Fisher information measure
  • Sample quantiles

ASJC Scopus subject areas

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


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