Asymptotically Normal Estimators for Zipf’s Law

Mikhail Chebunin () and Artyom Kovalevskii ()
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Mikhail Chebunin: Sobolev Institute of Mathematics
Artyom Kovalevskii: Novosibirsk State University

Sankhya A: The Indian Journal of Statistics, 2019, vol. 81, issue 2, No 10, 482-492

Abstract: 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.

Keywords: Infinite urn scheme; Zipf’s law; Asymptotic normality.; Primary 62F10; Secondary 62F12 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13171-018-0135-9

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