Asymptotically Normal Estimators for Zipf’s Law

Research output: Contribution to journalArticle

Abstract

We study an infinite urn scheme with probabilities corresponding to a power function. Urns here represent words from an infinitely large vocabulary. We propose asymptotically normal estimators of the exponent of the power function. The estimators use the number of different elements and a few similar statistics. If we use only one of the statistics we need to know asymptotics of a normalizing constant (a function of a parameter). All the estimators are implicit in this case. If we use two statistics then the estimators are explicit, but their rates of convergence are lower than those for estimators with the known normalizing constant.

Original languageEnglish
Pages (from-to)482-492
Number of pages11
JournalSankhya A
Volume81
Issue number2
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Asymptotic normality.
  • Infinite urn scheme
  • Zipf’s law
  • Asymptotic normality
  • Primary 62F10; Secondary 62F12

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