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信息不足时的估计AI 解读

As a possible explanation for the existence of absurd UMVU estimators, a class of estimation problems is defined: estimating the probability of an “unobservable” event, for example, estimating the probability of an event of interest occurring over a long period of time from observations over a much shorter period. It is pointed out that in typical cases of this kind, no reasonable unbiased estimator can exist. Consideration of the maximum likelihood estimator suggests the…

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有限总体中样本均值的一项极小极大性质AI 解读

Consider the problem of estimating the mean of a finite population on the basis of a simple random sample. It was proved by Aggarwal (1954) that the sample mean minimizes the maximum expected squared error divided by the population variance $\tau^2$. Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying $\tau^2 \leq M$ for any fixed positive $M$. It is the purpose of this paper…

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非参数模型的描述统计：第三篇，离散程度AI 解读

Measures of dispersion are defined as functionals satisfying certain equivariance and order conditions. In the main part of the paper attention is restricted to symmetric distributions. Different measures are compared in terms of asymptotic relative efficiency, i.e., the inverse ratio of their standardized variances. The efficiency of a trimmed to the untrimmed standard deviation turns out not to have a positive lower bound even over the family of Tukey models. Positive…

非参数模型的描述统计（二）：位置AI 解读

Measures of location (without assumption of symmetry) are defined as functionals satisfying certain equivariance and order conditions. Three classes of such measures are discussed whose estimators are respectively linear functions of order statistics, $R$-estimators and $M$-estimators. It is argued that such measures can be compared in terms of the (asymptotic) efficiencies of their estimators. Of the three classes considered, it is found that trimmed expectations (and…

非参数模型的描述统计Ⅰ：导论AI 解读

An overview is given of an approach to the definition of descriptive characteristics of populations and to their estimation. The emphasis is on the robustness and efficiency of the estimators. Detailed summaries will be found in successive papers of the series dealing with the problems of location, scale and kurtosis.