Strong Consistency of the Good-Turing Estimator
Wagner, A.B.; Viswanath, P.; Kulkarni, S.R.
Information Theory, 2006 IEEE International Symposium on
Volume , Issue , 9-14 July 2006 Page(s):2526 - 2530
Digital Object Identifier   10.1109/ISIT.2006.262066
Summary: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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