Strong consistency of the good-turing estimator

被引：9

作者：

Wagner, Aaron B. ^{[1
]}

Viswanath, Pramod ^{[1
,2
]}

Kulkarni, Sanjeev R. ^{[3
]}

机构：

[1] Univ Illinois, Coordinated Sci Lab, 1101 W Springfield Ave, Urbana, IL 61801 USA

[2] Univ Illinois, Dept Elect Engn, Urbana, IL 61801 USA

[3] Princeton Univ, Dept EE, Princeton, NJ USA

来源：

2006 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1-6, PROCEEDINGS | 2006年

基金：

美国国家科学基金会;

关键词：

D O I：

10.1109/ISIT.2006.262066

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

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.

引用

下载

页码：2526 / +

页数：2

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