罕见事件情形下的典范估计
Canonical Estimation in a Rare-Events Regime
摘要：
我们提出了一个一般的方法进行统计推断内的“罕见事件制度”，最近提出的瓦格纳，Viswanath和Kulkarni。我们的方法可以很容易地建立一个非常大的一类典型的估计问题，在一个大的字母设置一致的估计。这些问题包括在原来的论文中研究，如熵和概率估计，除了许多其他有趣的。我们通过一致地估计字母表的大小和概率范围来特别说明这种方法。首先，我们提出了一个抽象的方法的基础上构建一个概率测度所需的渐近性质。然后，我们展示了两个具体的建设铸造良好的图灵估计作为一个伪经验的措施，并通过使用混合模型估计理论。
英文摘要：
We propose a general methodology for performing statistical inference within a `rare-events regime' that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish consistent estimators for a very large class of canonical estimation problems, in a large alphabet setting. These include the problems studied in the original paper, such as entropy and probability estimation, in addition to many other interesting ones. We particularly illustrate this approach by consistently estimating the size of the alphabet and the range of the probabilities. We start by proposing an abstract methodology based on constructing a probability measure with the desired asymptotic properties. We then demonstrate two concrete constructions by casting the Good-Turing estimator as a pseudo-empirical measure, and by using the theory of mixture model estimation.
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