Strong consistency of the good-turing estimator

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 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 languageEnglish (US)
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages2526-2530
Number of pages5
DOIs
StatePublished - 2006
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: Jul 9 2006Jul 14 2006

Publication series

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

Other

Other2006 IEEE International Symposium on Information Theory, ISIT 2006
CountryUnited States
CitySeattle, WA
Period7/9/067/14/06

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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    Wagner, A. B., Viswanath, P., & Kulkarni, S. R. (2006). Strong consistency of the good-turing estimator. In Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006 (pp. 2526-2530). [4036427] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2006.262066