TY - GEN

T1 - Strong consistency of the good-turing estimator

AU - Wagner, Aaron B.

AU - Viswanath, Pramod

AU - Kulkarni, Sanjeev R.

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - 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.

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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U2 - 10.1109/ISIT.2006.262066

DO - 10.1109/ISIT.2006.262066

M3 - Conference contribution

AN - SCOPUS:39049163490

SN - 1424405041

SN - 9781424405046

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2526

EP - 2530

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

T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006

Y2 - 9 July 2006 through 14 July 2006

ER -