随机变量拟算术均值的极限定理及其在柯西分布点估计中的应用

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Brazilian Journal of Probability and Statistics Pub Date : 2021-04-13 DOI:10.1214/22-BJPS531

Y. Akaoka, K. Okamura, Y. Otobe

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引用次数: 7

摘要

摘要我们建立了随机变量拟算术平均的一些极限定理。这类均值包括算术均值、几何均值和调和均值。我们的特点是允许拟算术平均的生成元是复值的，这使得考虑可能取负值的随机变量的拟算术平均成为可能。极限定理的动机是找到柯西分布参数的简单估计量。通过应用极限定理，我们得到了Cauchy分布的位置和尺度参数联合的一些闭形式无偏强相合估计量，这些估计量易于计算和分析。

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Limit theorems for quasi-arithmetic means of random variables with applications to point estimations for the Cauchy distribution

Abstract. We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasiarithmetic means are allowed to be complex-valued, which makes considerations for quasi-arithmetic means of random variables which could take negative values possible. Our motivation for the limit theorems is finding simple estimators of the parameters of the Cauchy distribution. By applying the limit theorems, we obtain some closed-form unbiased strongly-consistent estimators for the joint of the location and scale parameters of the Cauchy distribution, which are easy to compute and analyze.

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来源期刊

Brazilian Journal of Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.60

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.