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首页> 外文期刊>Journal of Mathematical Sciences >THE LIMIT DISTRIBUTION OF UNBIASED ESTIMATES OF INTEGRAL FUNCTIONALS WHOSE SUFFICIENT STATISTICS OF THE UNKNOWN PARAMETER ARE THE MINIMUM AND THE MAXIMUM
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THE LIMIT DISTRIBUTION OF UNBIASED ESTIMATES OF INTEGRAL FUNCTIONALS WHOSE SUFFICIENT STATISTICS OF THE UNKNOWN PARAMETER ARE THE MINIMUM AND THE MAXIMUM

机译：未知函数的充分统计量为最小值和最大值的整数函数的无偏差估计的极限分布

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摘要

Unbiased estimates have been successfully used in the solution of different tasks for a rather long time. At present, there are works containing tables of unbiased estimates of parameters and functions from many probability distributions (see, for example, ). The problem of the discovery of asymptotic distributions of unbiased estimates even by a sample of fixed volume has been less studied. The absence of a general result of this nature often serves as a basis for the use of estimations of the maximum likelihood as statistical estimations of unknown values. Moreover, it was shown in that an unbiased estimate like an estimate of the maximum likelihood is asymptotically normal and asymptotically effective in very natural conditions. Moreover, regular families of distributions, the sufficient statistics of which is a sample mean, were considered in them. Thus, normalizing constants, providing a convergence to the nondegenerated normal distributions, were found in explicit form. In this work, the limit behavior of unbiased estimates of characteristics of nonregular distribution families, the sufficient statistics of which is a pair - the minimum and maximum of a nondependent repeat sample - is studied. Results were partially announced in. The case where the minimum or maximum is a sufficient statistics was considered in.
机译：长期以来，无偏估计已成功用于解决不同任务。当前，有一些作品包含来自许多概率分布的参数和函数的无偏估计表（例如，参见）。甚至通过固定体积的样本来发现无偏估计的渐近分布的问题也很少研究。缺乏这种性质的一般结果通常可以作为使用最大似然估计作为未知值的统计估计的基础。此外，还显示出，无偏估计（如最大似然估计）在非常自然的条件下渐近正常且渐近有效。此外，还考虑了常规的分布族，其中充分的统计数据是样本平均值。因此，发现显式形式的归一化常数为未退化的正态分布提供了收敛。在这项工作中，研究了非正态分布族的特征的无偏估计的极限行为，该非正态分布族的足够统计量是一对-非依赖性重复样本的最小值和最大值。结果已部分公布。考虑了最小值或最大值是足够的统计量的情况。

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