球面上fr均值定理和中心极限定理的性质

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI:10.1214/21-bjps499

Do Tran

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引用次数: 3

摘要

我们计算了具有绝对连续和旋转对称概率分布的球上fr切特函数的高阶导数。结果包括:(i)一个检验对称分布的模态是否为局部fr平均模态的实际条件;(ii)具有实际假设和显式极限分布的球的中心极限定理;(iii)对于具有绝对连续和旋转对称分布的球体是否可以发生涂抹效应的问题的回答:通过本文提出的方法，它至少可以在4维上发生。

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Behavior of the Fréchet mean and Central Limit Theorems on spheres

We compute higher derivatives of the Fréchet function on spheres with an absolutely continuous and rotationally symmetric probability distribution. Consequences include (i) a practical condition to test if the mode of the symmetric distribution is a local Fréchet mean; (ii) a Central Limit Theorem on spheres with practical assumptions and an explicit limiting distribution; and (iii) an answer to the question of whether the smeary effect can occur on spheres with absolutely continuous and rotationally symmetric distributions: with the method presented here, it can in dimension at least 4.

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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.