Standard

Asymptotically Normal Estimators for Zipf’s Law. / Chebunin, Mikhail; Kovalevskii, Artyom.

In: Sankhya A, Vol. 81, No. 2, 01.12.2019, p. 482-492.

Research output: Contribution to journal › Article › peer-review

Harvard

Chebunin, M & Kovalevskii, A 2019, 'Asymptotically Normal Estimators for Zipf’s Law', Sankhya A, vol. 81, no. 2, pp. 482-492. https://doi.org/10.1007/s13171-018-0135-9

APA

Chebunin, M., & Kovalevskii, A. (2019). Asymptotically Normal Estimators for Zipf’s Law. Sankhya A, 81(2), 482-492. https://doi.org/10.1007/s13171-018-0135-9

Vancouver

Chebunin M, Kovalevskii A. Asymptotically Normal Estimators for Zipf’s Law. Sankhya A. 2019 Dec 1;81(2):482-492. doi: 10.1007/s13171-018-0135-9

Author

Chebunin, Mikhail ; Kovalevskii, Artyom. / Asymptotically Normal Estimators for Zipf’s Law. In: Sankhya A. 2019 ; Vol. 81, No. 2. pp. 482-492.

BibTeX

@article{7107defbca4d4f8aa4ae3e98d68bca39,
title = "Asymptotically Normal Estimators for Zipf{\textquoteright}s Law",
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 = "Asymptotic normality., Infinite urn scheme, Zipf{\textquoteright}s law, Asymptotic normality, Primary 62F10; Secondary 62F12",
author = "Mikhail Chebunin and Artyom Kovalevskii",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s13171-018-0135-9",
language = "English",
volume = "81",
pages = "482--492",
journal = "Sankhya A",
issn = "0976-836X",
publisher = "Springer India",
number = "2",

}

RIS

TY - JOUR

T1 - Asymptotically Normal Estimators for Zipf’s Law

AU - Chebunin, Mikhail

AU - Kovalevskii, Artyom

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Asymptotic normality.

KW - Infinite urn scheme

KW - Zipf’s law

KW - Asymptotic normality

KW - Primary 62F10; Secondary 62F12

UR - http://www.scopus.com/inward/record.url?scp=85049888530&partnerID=8YFLogxK

U2 - 10.1007/s13171-018-0135-9

DO - 10.1007/s13171-018-0135-9

M3 - Article

AN - SCOPUS:85049888530

VL - 81

SP - 482

EP - 492

JO - Sankhya A

JF - Sankhya A

SN - 0976-836X

IS - 2

ER -

ID: 14869798