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Asymptotically Normal Estimators for Zipf’s Law

Author

Listed:
  • Mikhail Chebunin

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Artyom Kovalevskii

    (Novosibirsk State University
    Novosibirsk State Technical University)

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.

Suggested Citation

  • Mikhail Chebunin & Artyom Kovalevskii, 2019. "Asymptotically Normal Estimators for Zipf’s Law," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 482-492, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0135-9
    DOI: 10.1007/s13171-018-0135-9
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    References listed on IDEAS

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    1. Chebunin, Mikhail & Kovalevskii, Artyom, 2016. "Functional central limit theorems for certain statistics in an infinite urn scheme," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 344-348.
    2. Paul Travis Nicholls, 1987. "Estimation of Zipf parameters," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 38(6), pages 443-445, November.
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