Strong consistency of the good-turing estimator

Aaron B. Wagner; Pramod Viswanath; Sanjeev R. Kulkarni

doi:10.1109/ISIT.2006.262066

Strong consistency of the good-turing estimator

Aaron B. Wagner, Pramod Viswanath, Sanjeev R. Kulkarni

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

18 Scopus citations

Abstract

We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no symbol appears frequently in the string. This is accomplished by allowing the distribution to change with the block length. Under a natural convergence assumption on the sequence of underlying distributions, we show that the total probabilities converge to a deterministic limit, which we characterize. We then show that the Good-Turing total probability estimator is strongly consistent.

Original language	English (US)
Title of host publication	Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages	2526-2530
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2006.262066
State	Published - 2006
Event	2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States Duration: Jul 9 2006 → Jul 14 2006

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8101

Other

Other	2006 IEEE International Symposium on Information Theory, ISIT 2006
Country/Territory	United States
City	Seattle, WA
Period	7/9/06 → 7/14/06

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2006.262066

Cite this

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title = "Strong consistency of the good-turing estimator",

abstract = "We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no symbol appears frequently in the string. This is accomplished by allowing the distribution to change with the block length. Under a natural convergence assumption on the sequence of underlying distributions, we show that the total probabilities converge to a deterministic limit, which we characterize. We then show that the Good-Turing total probability estimator is strongly consistent.",

author = "Wagner, {Aaron B.} and Pramod Viswanath and Kulkarni, {Sanjeev R.}",

year = "2006",

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language = "English (US)",

isbn = "1424405041",

series = "IEEE International Symposium on Information Theory - Proceedings",

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Wagner, AB, Viswanath, P & Kulkarni, SR 2006, Strong consistency of the good-turing estimator. in Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006., 4036427, IEEE International Symposium on Information Theory - Proceedings, pp. 2526-2530, 2006 IEEE International Symposium on Information Theory, ISIT 2006, Seattle, WA, United States, 7/9/06. https://doi.org/10.1109/ISIT.2006.262066

Strong consistency of the good-turing estimator. / Wagner, Aaron B.; Viswanath, Pramod ; Kulkarni, Sanjeev R.
Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006. 2006. p. 2526-2530 4036427 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no symbol appears frequently in the string. This is accomplished by allowing the distribution to change with the block length. Under a natural convergence assumption on the sequence of underlying distributions, we show that the total probabilities converge to a deterministic limit, which we characterize. We then show that the Good-Turing total probability estimator is strongly consistent.

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BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006

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Y2 - 9 July 2006 through 14 July 2006

ER -

Strong consistency of the good-turing estimator

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