Strong Consistency of the Good-Turing Estimator

Details Strong Consistency of the Good-Turing Estimator Strong Consistency of the Good-Turing Estimator

2006-07-05

arxiv.org/abs/cs/0607014v1

Computer Science

Information Theory

To appear at IEEE ISIT 2006

Scientific paper

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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