Strong Consistency of the Good-Turing Estimator
Strong Consistency of the Good-Turing Estimator
复制标题
Good-Turing 估计器的强一致性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Kulkarni
中科院分区：
文献类型：
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作者：
Aaron B. Wagner;P. Viswanath;S. Kulkarni
我们考虑估计在独立同分布字符串中以给定频率出现的所有符号的总概率的问题。分布未知的随机变量。我们关注块长度很大但字符串中没有频繁出现的符号的情况。这是通过允许分布随块长度变化来实现的。在对基础分布序列的自然收敛假设下，我们表明总概率收敛到我们所描述的确定性极限。然后我们证明古德图灵总概率估计是强一致的
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