Abstract

An asymptotical approach to the statistical estimation problem is considered under the assumption that the number of observations is a random variable. This leads to distributions with heavy tails and changes in the efficiency of the normally used statistical procedures. Statistical estimates based on random-size and nonrandom-size samples are asymptotically compared against one another. The concept of asymptotic deficiency (the number of additional observations needed for a given estimate to achieve the same quality as the optimum estimate) is used to do so. Asymptotic expansions are also obtained for the risk functions of estimates based on random-size samples.

中文翻译：

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基于随机样本的估计风险

摘要

在观察数是随机变量的假设下，考虑采用统计方法的渐近方法。这将导致分布繁重的尾巴，并改变通常使用的统计程序的效率。将基于随机大小和非随机大小样本的统计估计值渐近地相互比较。渐近缺陷的概念（给定估计值要达到与最佳估计值相同的质量所需的其他观察次数）可用于此目的。对于基于随机大小样本的估计的风险函数，也可以得到渐近展开。