Asymptotic Efficiency and Limiting Information
Asymptotic Efficiency and Limiting Information
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渐近效率和限制信息
DOI：
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发表时间：
1961
期刊：
影响因子：
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通讯作者：
Calyampudi R. Rao
中科院分区：
文献类型：
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作者：
Calyampudi R. Rao
在最近的一篇论文[15]中，作者给出了渐近有效性和一致性概念的新公式，这似乎对最大似然原理（m.l.）估计。在该论文中还尝试将渐近效率的概念与统计量中包含的每个观察值的限制信息联系起来，因为样本量趋于无穷大，关于未知参数0的信息在Fisher意义下定义[5]，[6]。本文的目的是继续研究前一篇论文，并进一步建立一些可能有助于理解m.l.的命题。估计方法。第一个命题涉及的条件下，iT，每个观察在统计量Tn的信息趋于i，在一个单一的观察，作为样本大小n -* -的信息。可以注意到，对于任何n，iT不能超过i。iT收敛到i的一个充分条件是
In a recent paper [15], the author gave new formulations of the concepts of asymptotic efficiency and consistency, which seem to throw some light on the principle of maximum likelihood (m.l.) in estimation. An attempt was also made in that paper to link up the concept of asymptotic efficiency with the limiting information per observation contained in a statistic, as the sample size tends to infinity, information on an unknown parameter 0 being defined in the sense of Fisher [5], [6]. The object of the present paper is to pursue the investigation of the earlier paper and establish some further propositions which might be of use in understanding the m.l. method of estimation. The first proposition is concerned with the conditions under which iT, the information per observation in a statistic Tn tends to i, the information in a single observation, as the sample size n -* -. It may be noted that iT cannot exceed i for any n. A sufficient condition for convergence of iT to i is