Cauchy分布拟算术平均的最大似然估计和一步估计的Bahadur效率

IF 0.6 4区数学 Q3 STATISTICS & PROBABILITY Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-11 DOI:10.1007/s10463-021-00818-y

Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe

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引用次数: 7

摘要

一些随机变量的拟算术均值很容易给出柯西分布的位置参数和尺度参数联合的无偏强一致闭型估计。研究了柯西分布的拟算术均值的一步估计。建立了极大似然估计量和一步估计量的Bahadur效率。我们还证明了均方误差的收敛速度达到cram r - rao界。我们的结果也适用于圆形柯西分布。

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Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution

Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy distribution. The one-step estimators of those quasi-arithmetic means of the Cauchy distribution are considered. We establish the Bahadur efficiency of the maximum likelihood estimator and the one-step estimators. We also show that the rate of the convergence of the mean-squared errors achieves the Cramér–Rao bound. Our results are also applicable to the circular Cauchy distribution .

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来源期刊

Annals of the Institute of Statistical Mathematics 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.

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